Question

impeded by the current the outing club took 4 hours and 24 minutes to paddle 11 km up the exeter river to their campsite last weekend. the next day the same current was with them and it took only 2 hours to make the return trip to campus. everyone paddled with the same intensity on both days. at what rate would the paddlers have traveled if there had been no current? what was the speed of the current

Answer 1

Answer: if there had been no current, the rate would have been 4 km/hr.

The rate of the current is 1.5km/hr

Step-by-step explanation:

Let x represent the speed of the boat in still water.

Let y represent the speed of the current.

Impeded by the current the outing club took 4 hours and 24 minutes(4 + 24/60 = 4.4 hours) to paddle 11 km up the exeter river to their campsite last weekend. This means that the total speed with which they travelled is (x - y) km/h

Distance = speed × time. Therefore

11 = 4.4(x - y)

Dividing through by 4.4, it becomes

2.5 = x - y - - - - - - - - - - -1

The next day the same current was with them and it took only 2 hours to make the return trip to campus. This means that the total speed with which they travelled is (x + y) km/h. The distance travelled is

11 = 2(x + y)

Dividing through by 2, it becomes

5.5 = x + y - - - - - - - - - - -2

Adding equation 1 to equation 2, it becomes

8 = 2x

x = 8/2 = 4

Substituting x = 4 into equation 1, it becomes

2.5 = 4 - y

y = 4 - 2.5

y = 1.5