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.
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The upstream speed of the boat is 40 km/hr and the speed of the boat in still water is 55 km/hr. What is the downstream speed of the boat?
A. 75 km/hr
B. 70 km/hr
C. 60 km/hr
D. 65 km/hr
