Question

Ashley goes to college in Minneapolis, 234 miles from her home in Sioux Falls. She wants her parents to bring her more winter clothes, so they decide to meet at a restaurant on the road between Minneapolis and Sioux Falls. Ashley and her parents both drove 2 hours to the restaurant. Ashley’s average speed was seven miles per hour faster than her parents’ average speed. Find Ashley’s and her parents’ average speed.

Short answer

Parents average speed$=55mph$

Ashley average speed$=62mph$

Step-by-step solution

Step 1. Given information

Let rbe the avarage speed

Ashley goes to college in Minneapolis, 234 miles from her home in Sioux Falls.

Ashley and her parents both drove 2 hours to the restaurant.

Ashley’s average speed was 7 miles per hour faster than her parents’ average speed.

Step 2. Finding Ashley’s and her parents’ average speed.

We are looking for their average speeds. Let’s let r represent the average speed of the parents. Since the Ashley’s speed is 7 mph faster, we represent that as $r+7$

Fill in the speeds into the chart as,

	Rate (mph)	Time (hours)	Distance(miles)
Ashley	$r+7$	2	$2(r+7)$
Parents	r	2	2r
			234

Multiply the rate times the time to get the distance.

The distance Ashley travelled plus the distance his parents travel must add up to 234 miles. So write it as,$2(r+7)+2r=234$

$$\begin{gathered} 2r+14+2r=234 \\ 4r+14=234 \\ 4r=234-14 \\ 4r=220 \\ r=\frac{220}{4} \\ r=55 \\ r+7=55+7 \\ =62 \end{gathered}$$

Parents average speed$55mph$

Ashley average speed $62mph$

Ashley drove distance 55mph(2 hours)=110 miles

Parents drove distance 62mph(2hours)=124 miles