Question

A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream.
(a) 2 hours
(b) 3 hours
(c) 4 hours
(d) 5 hours

Answer 1

Hint: First of all, find the downstream speed which is equal to the sum of speeds of the boat in still water and stream. Then use the formula, \[\text{time}=\dfrac{\text{distance}}{\text{speed}}\] to find the time taken by the boat to go 68 km downstream.

Complete step-by-step solution:
We are given that a boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, we have to find the time taken by the boat to go 68km downstream. We know that whenever the boat goes downstream, then the direction of the stream and direction of the boat is in the same direction. Hence, the stream supports the boat while going downstream. So, we get,
Downstream speed of boat = Speed of the boat in still water + Speed of the stream……(i)
Now, we are given that the speed of the boat in still water is 13 km/hr, and the speed of the stream is 4 km/hr. So, we get,
Downstream of the boat = 13 km/hr + 4 km/hr = 17 km/hr
Now, let us consider the time taken by the boat to go 68 km downstream as td.
Since, we know that \[\text{time}=\dfrac{\text{distance}}{\text{speed}}\], therefore by substituting the value of time = $t_d$, distance = 68 km and downstream speed of the boat = 17 km/hr in the above equation, we get,
\[\text{time}=\dfrac{\text{distance}}{\text{speed}}\]
\[t_d=\dfrac{68km}{17km/hr}\]
By simplifying the RHS of the above equation, we get $t_d$ = 4 hours.
So, the boat will take 4 hours to go 68km downstream.
Hence, the option (c) is the right answer.

Note: In these types of questions, students often get confused between downstream speed and upstream speed of the boat. So, they must note that when the boat and stream are in the same direction, then downstream speed is taken by addition of speeds whereas when the boat and stream are in the opposite direction, then upstream speed is taken which is equal to the difference of the speeds of the boat in still water and stream. Also, note that \[\text{time}=\dfrac{\text{distance}}{\text{speed}}\] is a universal equation that is used in all speed – time distance questions.