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

the speed of the motorboat was 90.313 mph

Explanation:

since the distance d covered for each watercraft is

d = v*t, where v = velocity and t = time spent in that watercraft

the difference in speed will be

v₂-v₁ = d₂/t₂ - d₁/t₁ = 10 mph

with the constraint

t₂ + t₁ = 4 hours → t₂ = 4 - t₁

where 2 represents motorboat and 1 jet ski

then

d₂/t₂ - d₁/t₁ = 10

d₂ / (4 - t₁) - d₁/t₁ = 10

d₂*t₁ - d₁ * (4 - t₁) = 10 * t₁ * (4 - t₁)

d₂*t₁ - 4*d₁ + d₁*t₁ = 40*t₁ - 10*t₁²

10*t₁² + (d₂+d₁-40) * t₁ - 4*d₁ = 0

replacing values of distances

10*t₁² + (d₂+d₁-40) * t₁ - 4*d₁ = 0

10*t₁² + (45+124 - 40) * t₁ - 4*124 = 0

10*t₁² + 129 * t₁ - 496 = 0

then

t₁ = [-129 + √ (129²+4*10*496) ] / (2*10) = 1.373 hours

therefore

v₁ = d₁/t₁ = 124 miles/1.373 hours = 90.313 mph

thus the speed of the motorboat was 90.313 mph