Find the speed of​ Tran's boat and the speed of the current.

Question

In his​ motorboat, Tran travels upstream at top speed to his favorite fishing​ spot, a distance of

30 ​miles, in 6 hours.​ Returning, he finds that the trip​ downstream, still at top​ speed, takes only

2.5 hours.

Find the speed of​ Tran's boat and the speed of the current.

Answer 1

d=rt, distance = rate of speed times time, b= boat speed, c = current speed

30 = 6(b-c) = 6b -6c

30 =2.5(b+c)= 2.5b + 2.5c

multiply the last equation by 6 and 1st equation by 2.5

180 = 15b + 15c

75 =15b - 15c add the two equations

255 = 30b

b = 255/30 = 8.5 mph for boat speed

or subtract the 2 equations

105 = 30c

c = 105/30 = 3.5 mph for the current speed

(8.5- 3.5)6 = 5(6) = 30 miles

(8.5+3.5)2.5 = 12(2.5) = 30 miles