Distance problem

Question

Jane took a boat upstream for 15 minutes. When she went back downstream at the same speed, it only took her 5 minutes. If the current is 3 km/h, what is the speed of the boat in still water? Thank you so much!

Answer 1

current = 3 kph

upstream took 15 minutes = 1/4 hour

downstream took 5 minutes = 1/12 hour

what is the boat's speed in still water??

d=rt distance = rate of speed times time

d = (r+3)(1/12) = (r-3)(1/4)

multiply by 12

r+3 = 3r-9

2r =9+3 = 12

r =12/2 = 6 kph = boat's speed in still water

Answer 2

Di stance = (Rate)(Time)

Let x = speed of boat in still water(km/hour). Speed of current = 3.

Speed downstream = x + 3 and time downstream = 5 min = (5/60) hr = (1/12) hr

Speed upstream = x - 3 and time upstream = 15 min = (15/60) hr = (1/4) hr

Distance upstream = Distance downstream

So, (1/4)(x - 3) = (1/12)(x + 3)

3(x - 3) = x + 3

2x = 12

x = 6 km/hr

Answer 3

This is a system of equations type of problem.

1. Lets define our variables.
2. Current is C. C = 3 km/h
3. Distance Covered is D. D is an unknown km.
4. Boat speed is B. B is an unknown km per hour.
5. Step: What are we looking for? We are looking to solve for the speed of the boat, B.
6. Lets set up our equations.
7. In the upstream direction. D km /[15 min / (60 min/1 h)] = B km/h - C km/h. Cleaned up this is 4*D = B - C
8. Note: The distance D was divided by the time it took to cover the distance. This makes it into a distance over time. Additionally, units need to be consistent, so the 15 minutes is converted into hours. This becomes 0.25 h.
9. Note: Since this is going upstream, we know the current is working against the boat speed. This is why it is B - C.
10. In the down stream direction: D km / [5 min / (60 min/1 h)] = B km/h + C km/h. Cleaned up this is 12*D = B + C.
11. We need to take one of the equations and solve for D and then insert it into the other equation.
12. Upstream equation: D = (B - C)/4
13. Inserting this into the down stream equations we get: 12* (B - C)/4 = B + C. Cleaned up this is 3B - 3C = B + C.
14. Now we solve the problem. C is known, so we take it's value and plug it back in, and then we solve for B.
15. 2* B = 4 * C. This means, B = 2 * C. Therefore B = 2 * 3. B = 6 km/h.
16. Lets test this value out in both the upstream equation and the down stream to make sure this is correct.
17. Upstream: 4 * D = B - C.
18. D = (B - C)/ 4
19. D = (6 - 3)/4.
20. D = 3/4 km.
21. Downstream: 12 * D = B + C
22. D = (B + C)/12
23. D = (6 + 3)/12
24. D = 3/4 km
25. Conclusion: If the water was still, the boat would be moving at 6 km/h.