Rekha walks from village X towards Y and Sunil walks from Y towards X, starting together. After they meet, Rekha needs 9 more hours to reach Y and Sunil needs 4 more hours to reach X. What is the ratio of Rekha's speed to Sunil's speed?

4 : 9

Correct answerYour answer

2 : 3

Correct answerYour answer

3 : 2

Correct answerYour answer

9 : 4

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

If they meet after $t$ hours, Rekha's part after meeting (9 h of her walking) equals Sunil's part before meeting ( $t$ h of his).
So $9a = tb$ and $4b = ta$ , where $a$ , $b$ are their speeds.
Dividing: $\frac{9a}{4b} = \frac{b}{a}$ , so $\frac{a^2}{b^2} = \frac{4}{9}$ .
$a : b = 2 : 3$ .

Worth noting

The shortcut is $\frac{a}{b} = \sqrt{\frac{t_{\text{Sunil}}}{t_{\text{Rekha}}}}$ . Writing $4 : 9$ forgets the square root; $3 : 2$ flips the ratio.

Concept: Speeds from the times taken after meeting: ratio = square root of the inverse time ratio
Typical timeTypical: 90 s
Your timeYours: —

Ten questions from Time, Speed & Distance, at your own pace.

Explanation