Question

A boat travels 140 miles downstream in the same amount of time as it travels 92 miles upstream. The speed of the current is 6mph. What is the speed of the boat

Answer 1

41mph downstream

17mph upstream

Explanation:

If the boat travels 140miles downstream, meaning with the current and the current speed is 6mph, We can determine the speed of the boat by calculating the time it takes for the boat to go upstream and downstream. Let x be the time for both upstream and downstream and y be the total speed of the boat:

Downstream:

`140/x+6=y`

upstream"

`92/x-6=y`

y is common:

`140/x+6=92/x-6`

solve for x:

`12\cdot{x}=140-92`

`x=4`

Therefore the speed of the boat upstream:

`140/4+6=y=41`

upstream

`92/4-6=y=17`

Answer 2

speed of the boat = 29 mph

Explanation:

In order to solve the problem, we need to recall the formula for speed (or velocity "v") of an object as the quotient between the distance (d) covered over the time (t) it takes to cover it:
`v=(d)/(t)`

Now we analyse the two different situations (downstream vs upstream) separately:

Downstream:

Considering that when the boat goes downstream (140 mile trip), it goes with the current, so its velocity (unknown v) couples (adds) to that of the current (6 mph) its total speed would be: v + 6 mph. Therefore we can use this information to write the equation for velocity given above, and solve for time:

`v+6=(140)/(t)\\t*(v+6)=140\\t=(140)/(v+6)`

Upstream:

In this case, the boat goes against the current, so its speed will be reduced by the current's speed of 6 mph, then its total speed will be: v - 6 mph. Recalling that in this case the boat travels 92 miles in the same time (t) it took it to do the downstream trip, we can write:

`v-6=(92)/(t)\\t*(v-6)=92\\t=(92)/(v-6)`

Now all we need to do is make these last two equations equal each other since the time used for each trip is the same. We can then solve for the actual speed (unknown v) of the boat:

`(140)/(v+6) = (92)/(v-6) \\140*(v-6)=92*(v+6)\\140v - 840=92v+552\\140v-92v=552+840\\48v=1392\\v=(1392)/(48) =29mph`