Question 1139720
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.