Simple algebra word problem

Question

Kady drove through the city for an hour. She drove for 2 hours on the highway, where her speed was 10 miles per hour faster than in the city. If she covered a total distance of 146 miles, what was her speed in the city?

Answer 1

Hi Sean,

 

This problem is relying on the fact that distance = rate x time (D=RT).

If we could find the distance Kady traveled on the highway and the distance she traveled in the city and add them together that total would be 146. 

 

So, let R=rate in the city. Since she drove for an hour in the city her city distance (D_c) is R(1).

Her rate on the highway was 10 mph greater than the city speed (R+10).

 

So, the distance she drove on the highway (for 2 hours) was D_h = 2(R+10).

 

Now we can write an equation where the only variable is R. 146 = 2(R+10) + R. Solve for R and you will have her rate in the city.

 

146=2R + 20 + R

146=3R + 20

126=3R

R=42

 

Check it out. 1 hour at 42 mph = 42 miles. 2 hours at 52 mph = 104 for a total of 146.