Question

A motorboat travels 440 km in eight hours going upstream and 510 km in six hours going down stream what is the rate of the boat in Still water and what is the rate of the current

Answer 1

Rate of boat in still water = 70 km/hr

Rate of current = 15 km/hr

Explanation:

Let the speed of motorboat in still water =
`u\ km/hr`

Let the speed of current =
`v\ km/hr`

Equivalent Speed upstream =
`(u-v)\ km/hr`

Equivalent Speed downstream =
`(u+v)\ km/hr`

Distance traveled upstream = 440 km

Time taken upstream = 8 hours

Using the formula:

`Speed = (Distance)/(Time)`

`u-v = (440)/(8)\\\Rightarrow u -v=55 ..... (1)`

Distance traveled downstream = 510 km

Time taken downstream = 6 hours

`u +v = (510)/(6)\\\Rightarrow u+v=85 ...... (2)`

Adding (1) and (2):

`2u = 140\\\Rightarrow u = 70\ km/hr`

By equation (1):

`v = 85-70\\\Rightarrow v =15\ km/hr`

Therefore, the answer is:

Rate of boat in still water = 70 km/hr

Rate of current = 15 km/hr