A boat sails 40 km downstream and then 40 km upstream in a river. The boat's speed in still water is 12 km/hr and the speed of the stream is 4 km/hr. How much time does the boat take to cover the entire distance (both upstream and downstream)?
7.5 hours
To determine how much time the boat takes to cover the entire distance of 40 km downstream and 40 km upstream, we need to calculate the time taken for each journey and then sum these times. Here's the step-by-step solution:
- Calculate the downstream speed: The speed of the boat in still water is 12 km/hr, and the speed of the stream is 4 km/hr. The downstream speed is the sum of the boat's speed and the stream's speed.
\(v_{\text{downstream}} = v_{\text{boat}} + v_{\text{stream}} = 12 \,\text{km/hr} + 4 \,\text{km/hr} = 16 \,\text{km/hr}\)
- Calculate the time taken to travel downstream: The downstream distance is 40 km. Time is calculated using the formula:
\(t_{\text{downstream}} = \frac{\text{distance}}{\text{speed}} = \frac{40 \,\text{km}}{16 \,\text{km/hr}} = 2.5 \,\text{hours}\)
- Calculate the upstream speed: The upstream speed is the difference between the boat's speed and the stream's speed.
\(v_{\text{upstream}} = v_{\text{boat}} - v_{\text{stream}} = 12 \,\text{km/hr} - 4 \,\text{km/hr} = 8 \,\text{km/hr}\)
- Calculate the time taken to travel upstream: The upstream distance is 40 km.
\(t_{\text{upstream}} = \frac{\text{distance}}{\text{speed}} = \frac{40 \,\text{km}}{8 \,\text{km/hr}} = 5 \,\text{hours}\)
- Calculate the total time for the round trip: Add the times for both the downstream and upstream journeys.
\(t_{\text{total}} = t_{\text{downstream}} + t_{\text{upstream}} = 2.5 \,\text{hours} + 5 \,\text{hours} = 7.5 \,\text{hours}\)
Therefore, the total time taken for the boat to cover the entire journey, both upstream and downstream, is 7.5 hours.
Important Questions from Boat and River
A boat goes 30 km upstream in 3 hours and downstream in 1 hour. How much time (in hours) will this boat take to cover 60 km in still water?
The speed of a motorboat in still water is 20 km/h. It travels 150 km downstream and then returns to the starting point. If the round trip takes a total of 16 hours, what is the speed (in km/h) of the flow of river?
The time taken by a boat to travel 13 km downstream is the same as time taken by it to travel 7 km upstream. If the speed of the stream is 3 km/h, then how much time (in hours) will it take to travel a distance of 44.8 km in still water?
A man can row a distance of 8 km downstream in a certain time and can row 6 km upstream in the same time. If he rows 24 km upstream and the same distance downstream in \(1\frac{3}{4}\) hours, then the speed (in km/h) of the current is:
A boat goes 27 km upstream and 33 km downstream in 6 hours. In the same time it can go 36 km upstream and 22 km downstream. How much time will it take to go 36 km upstream and 44 km downstream?
