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Popular Word Problems >

Mr. Bliss traveled 150 miles at a certain average rate. By increasing his rate 15 mph, he traveled 225 miles in the same time he spent on the 150 mile trip. Find his average rate on the trip.

Solution

M r . Bl i ss t r a v e l e d 150 mi l es a t a cer t ain a v er a g e r a t e . B y in cre a s in g hi s r a t e 15 m p h, h e t r a v e l e d 225 mi l es in t h e s am e t im e h e s p e n t o n t h e 150 mi l e t r i p . F in d hi s a v er a g e r a t e o n t h e t r i p .

Solution

trip 2 speed : 22.5

Solution steps

Given Speed:

trip 1 : 15

Given Distance:

trip 1 : 150

trip 2 : 225

Represent the time in terms of

x :

trip 1 : t_{2}

trip 1 Speed 15 Time t_{2} Distance 150

Write an equation for trip 1Distance = Speed

\cdot

Time

150 = 15 x

Solve for

x, 150 = 15 \cdot x : x = 10

time : 10

Represent the speed in terms of

y :

trip 2 : y

trip 2 Speed y Time 10 Distance 225

Write an equation for trip 2Distance = Speed

\cdot

Time

225 = y \cdot 10

Solve for

y, 225 = y \cdot 10 : y = \frac{45}{2}

\frac{45}{2} = 22.5

trip 2 speed : 22.5

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