Question

In a 500 m race, the ratio of the speeds of A and B is 3:4. A has a start of 140 m. Then, A wins by

Answer 1

To solve this problem we need to totally understand the problem carefully and should know what is actually happening. Given that there is a running race of 500 m. There are two players A and B participating in the running race. Also given the ratio of the two players running speed. The player A is at some point in the race, and we have to find out by how much distance from player B does A win.

Complete step by step answer:
Given that it is a running race of 500 m.
Given A and B are two players given the ratio of the speeds of A and B is 3:4.
Also given that A has a start of 140 m.
The distance A need to cover in order to reach 500 m is given by :
$\Rightarrow (500 - 140)$m
$\Rightarrow 360$m
$\therefore$The distance A needs to cover to reach the end of 500 m, i.e, is 360 m.
Given that the ratio of speeds of players A and B are 3:4
That is if A covers 3 m, then B covers 4 m.
So if A covers 360 m, then B covers the distance of , which is given below:
$\Rightarrow 360 \times \left( {\dfrac{4}{3}} \right) = 480$m.
$\therefore$ If A covers 360 m, then B covers 480 m.
That is when A reaches the end, then B is still behind A by:
$\Rightarrow (500 - 480)$m
$\Rightarrow 20$m
As B is behind A by 20 m.
Which means that A is ahead of B by 20 m.
$\therefore$A wins by 20 m.

Player A wins by 20 m.

Note: Here we need to understand that the two players A and B have the difference in their speeds which is already given. The most important thing here is to understand that the meaning of the player A has a start of 140 m is that the player A is at 140 m at a particular instant in the race and we have to find out how much more distance he needs to cover to reach the end point of the race.