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 
<pre>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: {{{matrix(1,3, 240/S - 3, "=", 200/(S + 10))}}}
            240(S + 10) - 3S(S + 10) = 200S ------ Multiplying by LCD, S(S + 10)
             {{{matrix(5,3, 240S + "2,400" - 3S^2 - 30S, "=", 200S, 210S + "2,400" - 3S^2, "=", 200S, 0, "=", 3S^2 + 200S - 210S  - "2,400", 0, "=", 3S^2 - 10S - "2,400", 0, "=", 3S^2 - 90S + 80S - "2,400")}}}
                                   0 = 3S(S - 30) + 80(S - 30)
                                   0 = (S - 30)(3S + 80)
                                   0 = S - 30         or       0 = 3S + 80
         Speed of slower ship, or {{{highlight_green(matrix(1,4, S, "=", 30, "km/h"))}}}      or       S = {{{matrix(1,2, - 80/3, "km/h")}}} (ignore)</pre>