Question

Speed ratio of boats A, B and stream is 8 ∶ 5 ∶ 2. B is 51 km ahead of A and it takes A 8.5 hours to catch up to B if they are travelling upstream. Find the time for A to travel 70 km downstream. (in hours)

1. 1.5
2. 2.5
3. 3.5
4. 4.5
5. 5.5

Answer 1

Correct Answer - Option 3 : 3.5

Given:-

Speed ratio = 8 ∶ 5 ∶ 2

Time for A to catch up 51 km = 8.5 hours.

Formula and concept:-

Relative speed when both are going in same direction is difference of their speeds.

Speed = Distance/Time

Downstream speed = u + v

Upstream speed = u – v

u and v are boat and stream speeds.

Calculation:-

Let speeds be 8x, 5x and 2x.

Upstream speed of A = 8x – 2x = 6x

Upstream speed of B = 5x – 2x = 3x

Relative speed = 6x – 3x = 3x

ATQ,

3x = 51/8.5

3x = 6

x = 2.

Downstream speed of A = 8x + 2x = 20

Time for 70 km = 70/20 = 3.5 hours.