Solve.
-Sue rowed her boat across Lake Bend and back in 3 hours. If her rate returning was 2 mph less than the rate going, and if the distance each way was 7 miles, find her rate going.
A)5.5 mph
B)5.9 mph
C)1.5 mph
D)3.7 mph

Question

Quizplus · Accepted Answer

Let's call Sue's rate going "x" mph. Then her rate returning is "x-2" mph (since it's 2 mph less).

We know that the distance each way is 7 miles, so Sue travels a total of 14 miles (7 miles going and 7 miles returning).

We also know that she completes this entire round trip in 3 hours.

Using the formula:

distance = rate x time

we can set up two equations:

7 = x*time going

7 = (x-2)*time returning

We can solve for "time going" in the first equation:

time going = 7/x

And we can solve for "time returning" in the second equation:

time returning = 7/(x-2)

We know that the total time for the round trip is 3 hours, so we can set up another equation:

time going + time returning = 3

Substituting our expressions for "time going" and "time returning":

7/x + 7/(x-2) = 3

Multiplying both sides by x(x-2) to clear the denominators:

7(x-2) + 7x = 3x(x-2)

Expanding and simplifying:

14x - 14 = 3x^2 - 6x

3x^2 - 20x + 14 = 0

We can use the quadratic formula to solve for x:

x = (20 ± sqrt(20^2 - 4(3)(14))) / (2(3))

x ≈ 5.9 or x ≈ 1.5

We know that Sue's rate going can't be 1.5 mph (since the rate returning would be x-2 = -0.5 mph, which doesn't make sense). So the only reasonable choice is B) 5.9 mph.

Solve. -Sue Rowed Her Boat Across Lake Bend and Back in in 3