Question

If a boat travels 18 km more in downstream than in

upstream in 3 hr. and if the speed of the Boat in still

water is 20 km/hr. find the distance travelled by boat

in downstream in 4 hr. ?

(a) 86 (b) 92 (c) 68

(d) 96 (e) None of these​

Answer 1

Let the speed of the motor boat in still water = u km/h

Let the speed of tte stream = v km/h

Speed of the boat down stream = (u + v) km/h

Speed of the boat up stream = (u - v) km/h

Distance travelled downstream by in 3 hours = (3 h) × [(u + v) Ikm/h] = 3 (u +v) km ————(1)

Dtance travelled upstream in 3 hours = (3 h) × [(u - v) km/h] = 3 (u - v) km ——————————-(2)

According to the statement of the questions;

3 × [ (u + v) - (u - v)] = 18 km

3 [ u + v - u + v] = 18 km

6 v = 18 km

v = 3 km/h

The speed of the stream = 3 km/h

Speed of the boat downstream = 20 km/h + 3 km/h = 23 km/h

The distance travelled downstream by the boat in 4 h = 4 h × ( 23) km/h = 92 km.