In his motorboat, Bill Ruhberg travels upstream at top speed to his favorite fishing spot, a distance of 24 mi, in 2 hr. Returning, he finds that the trip downstream, still at top speed, takes only 1.5 hr. Find the rate of Bill's boat and the speed of the current. Let x = the rate of the boat in still water and y = the rate of the current.
Accepted Solution
A:
Answer:Rate of Bill's boat = 14 miles per hourSpeed of the current = 2 miles per hourStep-by-step explanation:Let x = the rate of the boat in still water and y = the rate of the current.Distance traveled = 24 milesTime taken for upstream motion = 2 hourTime taken for downstream motion = 1.5 hourVelocity of upstream motion = x - yVelocity of downstream motion = x + yWe have Displacement = Time x VelocityUpstream motion 24 = 2(x-y) x - y = 12 ----------------------------eqn 1Downstream motion 24 = 1.5(x+y) x + y = 16 ----------------------------eqn 2eqn 1 + eqn 2 2 x = 28 x = 14 miles per hourSubstituting in eqn 2 14 + y = 16 y = 2 miles per hourRate of Bill's boat = 14 miles per hourSpeed of the current = 2 miles per hour