Question

In a 600 m race, P gives Q a start of 200 m. Ratio of the speeds of P and Q is 5:4. Who wins the race? By what distance does the winner beat the loser?​

Answer 1

Answer:

Q will win the race by 100m

Step-by-step explanation:

Distance to be covered by P (D1) = 600m

Distance to be covered by Q (D2) = 400m

Speed ratio P/Q = 5/4 =5x/4x

We know, Speed = Distance/Time

=> Time = Distance/Speed

=> Time taken by P (T1) = D1/5x

=> T1 = 600/5x

= 120/x

=> Time taken by Q (T2) = D1/4x

=> T2 = 400/4x

= 100/x

Here, T1>T2 which mean time taken by P to complete the race is more than Q. Hence Q win the race.

Time difference = 120/x -100/x = 20/x

Distance covered by P in 20/x =Speed x Time

= 5x X 20/x

= 100 m

Answer 2

Answer:

Q wins the race. Q will beat P by a distance of 100m

Step-by-step explanation:

Given:

Distance to be covered by P(D₁) = 600m

Distance to be covered by Q(D₂) = 400m

Speed ratio of P: Q - 5:4 = 5x:4x

To find: Winner of race

Solution:
$Speed=Distance/Time$

∴ $Time=Distance/Speed$

For P,

Time(T₁) = 600/5x=120/x

For Q,

Time(T₂) = 400/4x=100/x

Since T₁ is greater than T₂, P took longer to finish the race.

Thus Q won the race.

T₁-T₂=20/x

∴ Distance covered by P in 20x = 20/x*5x = 100

Thus, Q won by a distance of 100m