Speed of the slower ship

Question

Two ships traveling from destination A to destination B differ in average speed by 10 kph. The slower ship takes 3 hours longer to travel a 240-Kilometer route than for the faster ship to travel a 200-kilometer route. Find the Speed of the slower ship.

Answer 1

Distance = rate(time) ... d = rt

 

Faster ship: rate=r, time=t hours

200 = rt

 

Slower ship: rate=r-10, time=t+3 hours

240 = (r-10)(t+3)

 

t = 200/r from 1st equation.

Substitute into 2nd equation:

 

240 = (r- 10)(200/r + 3)

240 = 200 + 3r - 2000/r - 30

240 = 3r - 2000/r + 170

clear fractin, multiply through by r:

240r = 3r² - 2000 + 170r

3r² - 70r - 2000 = 0

 

r = [-b±√(b²-4ac)]/(2a)

a = 3, b = -70, c = -2000

 

r = [70±√((-70)²-4(3)(-2000))]/(2(3))

 

r = (70 ±√28900)/6

r = (70±170)/6

discarding the negative

r = 240/6 = 40 km/hr

 

slower ship rate = r-10 = 30 km/hr