A steamboat travels 11 ​km/h faster than a freighter. The steamboat travels 100 km in the same time the freighter travels 78 km. Find the speed of each boat.

Question

A steamboat travels 11 ​km/h faster than a freighter. The steamboat travels 100 km in the same time the freighter travels 78 km. Find the speed of each boat.

The speed of the freighter is _____ ​km/h.

​(Simplify your​ answer.)

The speed of the steamboat is _______ ​km/h.

​(Simplify your​ answer.)

Answer 1

Let

r = the speed of the freight.

r + 11 = the speed of the steamboat

D_s = Distance traveled by steamboat

D_f = Distance traveled by freighter.

Remember the formula D = rt? Since the travel times of both steamboat and freighter are the same, we need to get the value of t in terms of D and r.

t = D/r

Following the formula, the time traveled by the steamboat can be represented as

100/(r+11)

And the time traveled by the freighter can be represented as

78/r

Since both travel times are the same, we can put those two representations equal to each other:

100/(r +11) = 78 / r

100r = 78 (r + 11)

100r = 78r + 858

22r = 858

r= 39 km/hr is the speed of the freight

r + 11 = 50 km/hr is the speed of the steamboat

Answer 2

Let x = speed (rate) of freighter

Let x + 11 = speed of steamboat

Use the formula: time = distance/rate

Steamboat: time = 100/(x+11)

Freighter: time = 78/x

78/x= 100/(x+11)

Cross multiply and solve for x. x = 39

Therefore the speed of the freighter is 39 km/h

The speed of the steamboat is 50 km/h