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April 27th, 2018, 09:14 AM   #1
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How to solve this "time and distance" concept problem?

A and B start together from city P to city Q with respective speeds in the ratio 3:2 . If B takes $2\dfrac{1}{2}$ hours more than A to reach Q, then how much time does A take to reach Q?

Ans: 5 hours

I am stuck at this problem, I know distance =speed x time.

Respective speed means 3x -2x = x
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April 27th, 2018, 09:44 AM   #2
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respective speeds in the ratio 3:2 means that if A travels with speed $v$ then B travels with speed $\dfrac 2 3 v$

let $d$ be the distance between P and Q

$\dfrac{d}{\frac 2 3 v}= \dfrac{d}{v}+\dfrac 5 2$

$\dfrac 3 2 \dfrac d v - \dfrac d v = \dfrac 5 2$

$\dfrac 1 2 \dfrac d v = \dfrac 5 2$

$T = \dfrac d v = 5$

and $T$ is the time it takes A to get from P to Q
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April 27th, 2018, 10:54 AM   #3
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As the speeds of A and B are in the ratio 3:2, their times are in the ratio 2:3 respectively.
Those times differ by 1, which you are told represents 2 1/2 hours, so A's time is 2 times 2 1/2 hours, which is 5 hours. This assumes that they take the same route from city P to city Q (or routes of the same length).
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