Question

Two ferries travel across a lake 50 miles wide. One ferry goes 5 miles per hour slower than the other. If the slower ferry leaves 1 hour earlier than the faster, but both arrive at the same time, what is the speed of the slower ferry

Answer 1

Answer:

Step-by-step explanation:

Let x be the speed of first ferry.

Then the speed of second slower ferry is x-5 (since 5 miles per hour slower)

Time taken by first ferry = distance/speed = $\frac{50}{x}$

Time taken by second ferry = $\frac{50}{x-5}$

Since second ferry starts one hour early, difference in times is 1 hour.

$\frac{50}{x-5}-\frac{50}{x}=1\\50x-50(x-5)=x(x-5)\\250 = x^2-5x\\x^2-5x-250 =0\\(x-10)(x+5) =0\\x=18.5, -13.5$

Speed cannot be negative.

Hence answer is speed of the first ferry = 18.5 mph

and second ferry i.e. slower ferry is = 13.5 mph