Question

A boat traveling upstream has to reach its destination by 03:00 p.m. The boat started at 12 noon and was traveling with a speed of 10 km/hr in still water to cover one-fourth of the distance, after which the river started flowing 20% faster against the boat. What should be the percentage increase in the still water speed of the boat so as to reach just in time? Given that the speed of flow is 5 km/hr and the total distance to be covered is 20 km.

A. 20%
B. 25%
C. 30%
D. 35%

Answer 1

To reach the destination in time, the boat needs to increase its speed in still water by 140%.

Step-by-step explanation:

To reach the destination in time, the boat needs to increase its speed in still water. Let's first calculate the time it takes for the boat to cover one-fourth of the distance. The total distance is 20 km, so one-fourth of that is 5 km. At a speed of 10 km/hr, it would take the boat 0.5 hours (5/10 = 0.5) or 30 minutes to cover that distance.

After covering one-fourth of the distance, the river starts flowing 20% faster against the boat. So, the effective speed of the river would be 5 km/hr + 20% of 5 km/hr = 5 km/hr + 1 km/hr = 6 km/hr.

Now, let's calculate the remaining time for the boat to reach the destination. The remaining distance after covering one-fourth is 20 km - 5 km = 15 km. The boat is now moving against the flow of the river, so the effective speed of the boat is the speed of the boat in still water (let's call it v) minus the speed of the river (6 km/hr). The remaining time can be calculated using the formula: Time = Distance / Speed. So, the time it takes for the boat to cover the remaining distance is 15 km / (v - 6) km/hr.

Since the boat needs to reach the destination in time, the total time taken should be 5 hours. We can now set up the equation: 0.5 + (15 / (v - 6)) = 5. Solving this equation will give us the value of v, the speed of the boat in still water. Once we have v, we can calculate the percentage increase in the still water speed of the boat using the formula: ((v - 10) / 10) * 100.

To solve the equation, we can first multiply both sides by (v - 6) to get rid of the fraction: (v - 6)(0.5) + (15) = 5(v - 6). Simplifying this equation will give us: 0.5v - 3 + 15 = 5v - 30.

By further simplifying the equation, we get: -0.5v = -12. Rearranging it to isolate v, we find v = 24. So, the speed of the boat in still water should be 24 km/hr to reach the destination just in time.

Now, let's calculate the percentage increase in the still water speed of the boat: ((24 - 10) / 10) * 100 = 140%.