A boat can cover 120 km downstream in 2.5 hours, and the speed of the boat and speed of stream in the ratio 7:5. If the boat can cover d-24 km upstream in 7.5 hours, then find the time taken by the boat to cover d km in still water?

Given:

Downstream distance = 120 km, Time taken = 2.5 hours

Speed ratio of boat and stream = 7:5

Upstream distance = d - 24 km, Time taken = 7.5 hours

Formula used:

Speed downstream = (Speed of boat + Speed of stream)

Speed upstream = (Speed of boat - Speed of stream)

Speed = Distance / Time

Calculations:

Speed downstream = 120 km / 2.5 hours = 48 km/h

Let the speed of the boat = 7x and speed of stream = 5x

⇒ Speed downstream = 7x + 5x = 12x

⇒ 12x = 48

⇒ x = 4

Speed of boat = 7x = 7 × 4 = 28 km/h

Speed of stream = 5x = 5 × 4 = 20 km/h

Now, Speed upstream = Speed of boat - Speed of stream = 28 - 20 = 8 km/h

Distance upstream = d - 24 km, Time taken = 7.5 hours

Speed upstream = (d - 24) / 7.5

⇒ 8 = (d - 24) / 7.5

⇒ 8 × 7.5 = d - 24

⇒ 60 = d - 24

⇒ d = 84 km

Now, the time taken to cover d km in still water is given by:

Time = Distance / Speed of boat

Time = 84 km / 28 km/h = 3 hours

∴ The time taken by the boat to cover d km in still water is 3 hours.