Question 1139720: 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 by Theo(13342)   (Show Source):
You can put this solution on YOUR website! rate * time = distance.
for the motor boat, r * t = 124.
for the speed boat, (r + 10) * (4 - t) = 45
r is the rate of the motorboat.
r + 10 is the rate of the speed boat.
t is the time it takes the motorboat to travel 124 miles.
4 - t is the time it takes the speedboat to travel 45 miles.
this is because the total time travel by both is 4 hours, so, if the motorboat took t hours, the speedboat had to take 4 - t hours.
you have 2 equations that need to be solved simultaneously.
they are:
r * t = 124
(r + 10) * (4 - t) = 45
simplify the second equation and keep the first equation as is to get:
r * t = 124
4 * r - r * t + 40 - 10 * t = 45
add the two equations together to get:
4 * r + 40 - 10 * t = 169
subtract 40 from both sides of the equation to get:
4 * r - 10 * t = 129
solve for r to get r = (10 * t + 129) / 4
in the first equation of r * t = 124, replace r with (10 * t + 129) / 4 to get:
(10 * t + 129) / 4 * t = 124
multiply both sides of that equation by 4 to get (10 * t + 129) * t = 496
simplify to get 10 * t^2 + 129 * t = 496
subtract 496 from both sides of that equation to get:
10 * t^2 + 129 * t - 496 = 0
factor this quadratic equation to get:
t = -16 or t = 3.1
t has to be greater than 0, so t = 3.1 looks like a possible solution.
in the first equation of r * t = 124, replace t with 3.1 and solve for r to get r = 124 / 3.1 which results in r = 40.
your solution should be t = 3.1 hours and r = 40 miles per hour.
for the motorboat, r * t = 124 becomes 40 * 3.1 = 124 which becomes 124 = 124 which confirms the solution is good for the first equation.
for the jet ski, (r + 10) * (4 - t) = 45 becomes 50 * .9 = 45 which becomes 45 = 45 which confirms the solution is good for the second equation.
the solution looks good.
the solution is that byron's rate of speed in the motorboat is 40 miles per hour.
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