Arithmetic

Time, Speed & Distance

Medium

applied

A runs 9 times slower than B. If B gives A a start of 80 meters, how far must be the wining post on the tracks so that A and B reach there at the same time?

80 meters

9 meters

98 meters

90 meters

✅ Correct Option: 4

A runs 9 times slower than B. When B runs 9 meters, A runs 1 meter.

Speed ratio B : A = 9 : 1

Let A's speed = $1x$ and B's speed = $9x$

B gives A a start of 80 meters means A starts 80 meters ahead of B.

Let the winning post be at distance $d$ meters from the starting line.

B has to run: $d$ meters

A has to run: $(d - 80)$ meters

Since they reach at the same time:

Time for A = Time for B

$\frac{d - 80}{1x} = \frac{d}{9x}$

$\frac{d - 80}{x} = \frac{d}{9x}$

$d - 80 = \frac{d}{9}$

$9(d - 80) = d$

$9d - 720 = d$

$8d = 720$

$d = 90$

The winning post must be 90 meters from the starting line.

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Solution

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