Start by finding the distances traveled on the trips downstream and the upstream separately using the Distance Formula.
H
Practice makes perfect
We want to find how far a boat traveled on a river. We know that a boat took 4 hours on the trip downstream with a current of 6 kilometers per hour. Let x be the speed of the boat. Since the boat and the current were in the same direction on the trip downstream, we can express the total speed as x+6. Let's now find the distance traveled on the trip downstream.
Speed * Time = & Distance
⇓
( x+6) * 4 = & 4x+24
Great! We also know that the return trip took 10 hours against the same current, 6 kilometers per hour. This time, since the current and the boat were in the opposite directions, the total speed will be x-6. With this information we can find the distance traveled on the return trip following similar reasoning as for the trip downstream.
Speed * Time = & Distance
⇓
( x-6) * 10 = & 10x-60
Note that the distance traveled on the trip downstream and upstream needs to be the same. Therefore, we can write an equation to make them equal and then solve it to find the speed of the boat x.
With the speed of the boat, we can find the total distance traveled on this trip. Let's substitute x= 14 into one of the distance expressions. We can choose 4x+24.
The boat will travel 80 kilometers in one direction and 80 kilometers in the other direction.
Downstream:& 80
Upstream:& 80
Total Distance:& 160
In total the boat traveled 160 kilometers on the river, which corresponds to option H.
