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'Distance/Speed/Time' Word Problems Made Easy

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Re: 'Distance/Speed/Time' Word Problems Made Easy [#permalink] 'Distance/Speed/Time' Word Problems Made Easy   27 May 2021, 06:53
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You're so cool VeritasKarishma

I spent an hour on this concept and I think I got the intuition behind this.

Thanks so much!!!
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Re: 'Distance/Speed/Time' Word Problems Made Easy [#permalink] 'Distance/Speed/Time' Word Problems Made Easy   10 Sep 2021, 09:38
Can't thank enough for this compilation! Made it so clear
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Re: 'Distance/Speed/Time' Word Problems Made Easy [#permalink] 'Distance/Speed/Time' Word Problems Made Easy   10 Oct 2021, 12:14
Shortcut for Example 4. (Two cyclists start..........)

Solution:

Since the cyclists are moving in opposite directions - their relative speed (to each other) will be => 14+16 = 30mph
And we are given the total distance as 45 miles.
Now as Distance = Speed* Time
45 miles = 30 mph*T hrs
Solving, \( T=\frac{45}{30} => \frac{3}{2} = 1.5 hrs\)

Q.E.D.
:please:
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'Distance/Speed/Time' Word Problems Made Easy [#permalink] 'Distance/Speed/Time' Word Problems Made Easy   22 Mar 2023, 21:14
KarishmaB wrote:
VICKY69 wrote:
An executive drove from home at an average speed of 30 mph to an airport where a helicopter was waiting. The executive boarded the helicopter and flew to the corporate offices at an average speed of 60 mph. The entire distance was 150 miles; the entire trip took three hours. Find the distance from the airport to the corporate offices.

in the above example why cant distance row of flying cannot be taken as "150-x" and that of driving as "x" (in that table method scheme).because when i take as above mentioned then x equals to 30 which is wrong so plz can u help me that

distance-speed-time-word-problems-made-easy-87481


You can. x is the driving distance which you get as 30. So the flying distance was 150 - x = 120 (this is what is asked).

On the other hand, consider using ratios and weighted averages here.
Speeds are 30 and 60 and average speed is 150/3= 50 mph.
So ratio of time taken in each case = td/tf = (60 - 50)/(50 - 30) = 1:2
For 1 hour, he was driving and for 2 hours he was flying.






KarishmaB Can you please help to understand how do we take the average and calculate the ratios of time taken in step 2 .
I understand ratio of time taken in each case = total time driving : total time flying but I really don't understand how we used speeds to interprete the time . I 'm aware of the weighted average formula but unable to get the logic behind the step 2 . Would really appreciate if you can help.
Distance for which he flew = 60*2 = 120 miles

P.S. - Ask your doubt in the same thread as the original question. If you want some specific people to reply to your doubt, tag them in your post.
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'Distance/Speed/Time' Word Problems Made Easy [#permalink] 'Distance/Speed/Time' Word Problems Made Easy   Updated on: 08 Aug 2023, 02:23
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JulieLama wrote:
KarishmaB wrote:
VICKY69 wrote:
An executive drove from home at an average speed of 30 mph to an airport where a helicopter was waiting. The executive boarded the helicopter and flew to the corporate offices at an average speed of 60 mph. The entire distance was 150 miles; the entire trip took three hours. Find the distance from the airport to the corporate offices.

in the above example why cant distance row of flying cannot be taken as "150-x" and that of driving as "x" (in that table method scheme).because when i take as above mentioned then x equals to 30 which is wrong so plz can u help me that

distance-speed-time-word-problems-made-easy-87481


You can. x is the driving distance which you get as 30. So the flying distance was 150 - x = 120 (this is what is asked).

On the other hand, consider using ratios and weighted averages here.
Speeds are 30 and 60 and average speed is 150/3= 50 mph.
So ratio of time taken in each case = td/tf = (60 - 50)/(50 - 30) = 1:2
For 1 hour, he was driving and for 2 hours he was flying.






KarishmaB Can you please help to understand how do we take the average and calculate the ratios of time taken in step 2 .
I understand ratio of time taken in each case = total time driving : total time flying but I really don't understand how we used speeds to interprete the time . I 'm aware of the weighted average formula but unable to get the logic behind the step 2 . Would really appreciate if you can help.
Distance for which he flew = 60*2 = 120 miles

P.S. - Ask your doubt in the same thread as the original question. If you want some specific people to reply to your doubt, tag them in your post.


JulieLama

He drives for time td and flies for time tf.
His drive speed is 30 and fly speed is 60.
His average speed is given to be 50 (= Total distance 150 miles / Total time 3 hrs)

Note that average speed has 'time taken' as the weights.
This post discusses this in detail: https://anaprep.com/arithmetic-weights- ... d-average/

Hence, we can find the ratio of time taken by using the weighted avg formula.
Discussed here: https://www.youtube.com/watch?v=_GOAU7moZ2Q

Since we get the ratio of time taken as 1:2, out of total time of 3 hrs taken, for 1 hour, he was driving and for 2 hours he was flying.

Hence, fly distance = 2 * 60 = 120 miles

Originally posted by KarishmaB on 23 Mar 2023, 03:46.
Last edited by KarishmaB on 08 Aug 2023, 02:23, edited 1 time in total.
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Re: 'Distance/Speed/Time' Word Problems Made Easy [#permalink] 'Distance/Speed/Time' Word Problems Made Easy   23 Mar 2023, 04:20
Quote:

JulieLama

He drives for time td and flies for time tf.
His drive speed is 30 and fly speed is 60.
His average speed is given to be 50 (= Total distance 150 miles / Total time 3 hrs)

Note that average speed has 'time taken' as the weights.
This post discusses this in detail: https://anglesandarguments.com/blog-details/279

Hence, we can find the ratio of time taken by using the weighted avg formula.
Discussed here: https://anglesandarguments.com/blog-details/263

Since we get the ratio of time taken as 1:2, out of total time of 3 hrs taken, for 1 hour, he was driving and for 2 hours he was flying.

Hence, fly distance = 2 * 60 = 120 miles


KarishmaB Thank you so much for the reply . This blog has exactly what I was looking for.
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Re: 'Distance/Speed/Time' Word Problems Made Easy [#permalink] 'Distance/Speed/Time' Word Problems Made Easy   23 Mar 2024, 07:26
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Re: 'Distance/Speed/Time' Word Problems Made Easy [#permalink]
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