Proportion Rational equations

Question

Byron wanted to try out different water craft. He went 124 miles downstream in a motor boat and 45 miles downstream on a jet ski. His speed on the jet ski was 10 mph faster than in the motor boat. Byron spent a total of 4 hours on the water. What was his rate of speed, in miles per hour, in the motor boat?

Answer 1

Distance = (Rate)(Time), so Time = Distance/Rate

Let x = speed of motorboat

Then x+10 = speed of jet ski

Time in motorboat + Time on jet ski = 4

So, 124/x + 45/(x+10) = 4

124(x+10) + 45x = 4x(x+10)

169x + 1240 = 4x² + 40x

4x² - 129x - 1240 = 0

Now, use the quadratic formula to solve for x.