SOLUTION: There are two ships travelling from dumaguete to cagayan de oro differ in average speed by 10kph. The slower ship takes 3 hours longer to travel a 240km route than for the faster s

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Question 1196420: There are two ships travelling from dumaguete to cagayan de oro differ in average speed by 10kph. The slower ship takes 3 hours longer to travel a 240km route than for the faster ship to travel a 200km route. Find the speed of the slower ship. As a navigator, you are assigned to measure the speed of the slower ship.
Hint:construct an equation with time t as the variable
Found 3 solutions by ikleyn, Theo, MathTherapy:
Answer by ikleyn(52877)   (Show Source):
You can put this solution on YOUR website!
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There are two ships travelling from dumaguete to cagayan de oro differ in average speed by 10kph.
The slower ship takes 3 hours longer to travel a 240km route than for the faster ship
to travel a 200km route. Find the speed of the slower ship.
As a navigator, you are assigned to measure the speed of the slower ship.
Hint:construct an equation with time t as the variable
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Let x be the speed of the slower ship, in kilometers per hour. It covers the distance of 240 km in hours. The faster ship has the speed of (x+10) km/h and covers 200 km in hours. We are given the time is 3 hours longer than time . So we write this "time" equation - = 3 hours. +---------------------------------------------------+ | As soon as you got it, the setup is complete. | +---------------------------------------------------+ To solve the equation, multiply both sides by common denominator x*(x+10). You will get 240*(x+10) - 200x = 3x*(x+10) 240x + 2400 - 200x = 3x^2 + 30x 3x^2 - 10x + 2400 = 0 Solve this quadratic equation using the quadratic formula = = = . There are two roots, one is 30, the other is = -. We reject the negative root and accept the positive root. So, the ANSWER is 30 km/h for the slower ship. CHECK. Time for the slower ship is = 6 hours; time for the faster ship is = 5 hours. The difference of times is 8-5 = 3 hours, confirming the answer.

Solved and thoroughly explained.

Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website!
r*t=d
rate * time = distance
for the slower ship:
r*(t+3)=240
for the faster ship:
(r+10)*t=200
from the equation for the slower ship, solve for r to get:
r = 240/(t+3)
in the equation for the faster ship, replace r with 240/(t+3) to get:
(240/(t+3)+10)*t=200
multiply both sides of this equation by (t+3) to get:
(240 + 10*(t+3)*t = 200*(t+3)
simplify to get:
(240 + 10t + 30)*t = 200t + 600
simplify further to get:
240t + 10t^2 + 30t = 200t + 600
subtract the right side of the equation from both sides of the equation to get:
240t + 10t^2 + 30t - 200t - 600 = 0
combine like terms and reorder the equation in descending order of degreeto get:
10t^2 + 70t - 600 = 0
factor this quadratic equation to get:
t = 5 or -12.
t has to be positive, therefore t = 5
since r = 240/(t+3), then r = 240/8) = 30
you have t = 5 and r = 30
since r*t=d, you get:
30*8 = 240 for the faster ship.
40*5=200 for the slower ship.
numbers check out.
solution is that the speed of the slower ship is 30 kilometers per hour.

Answer by MathTherapy(10556)   (Show Source):
You can put this solution on YOUR website!

There are two ships travelling from dumaguete to cagayan de oro differ in average speed by 10kph. The slower ship takes 3 hours longer to travel a 240km route than for the faster ship to travel a 200km route. Find the speed of the slower ship. As a navigator, you are assigned to measure the speed of the slower ship.
Hint:construct an equation with time t as the variable

The given hint is one that I wouldn't recommend that you adhere to. The problem asks for the slower ship's speed and that's what I'd suggest that you focus on. Having said that, let the speed of the slower ship be S Then speed of the faster ship is S + 10 (their speeds differ by 10 km/h) With the slower taking 3 hours longer to travel 240 km than the faster takes to travel 200 km, we get the following TIME equation: 240(S + 10) - 3S(S + 10) = 200S ------ Multiplying by LCD, S(S + 10) 0 = 3S(S - 30) + 80(S - 30) 0 = (S - 30)(3S + 80) 0 = S - 30 or 0 = 3S + 80 Speed of slower ship, or or S = (ignore)