Doug, who runs track for his high school,
was challenged to a race by his younger
brother, Matt. Matt started running first,
and Doug didn’t start running until Matt
had finished a quarter-mile lap on the
school track. Doug passed Matt as they
both finished their sixth lap. If both boys
ran at a constant speed, with Doug running
2 miles an hour faster than Matt, what was
Matt’s speed?
Choices:
A) 10.5 miles per hour
B) 10 miles per hour
C) 9 miles per hour
D) 8 miles per hour
E) 7.5 miles per hour
Doug runs 2 miles an hour faster than Matt, so let Matt’s speed equal x miles per hour.   Then Doug’s speed equals x + 2 miles per hour. Each lap is one-quarter of a mile, so Doug   runs 1.5 miles in the time it takes Matt to run 1.25 miles. Place this information in a chart:   DOUGH RATE:x-2 TIME:1.5/1 DISTANCE:1.5   MATT RATE:X TIME:1.25/X DISTANCE:1.25   The two boys took the same amount of time from the time Doug started, so make an   equation by setting the two times in the chart equal to each other, and then solve for x:   1.5/X+2=1.25/X   1.5X=1.25(X+2)   1.5X=1.25X+2.5   0.25X=2.5   X=10   So Matt ran at 10 miles per hour.   correct answer 10 miles per hour)10 miles per hour
<result>B</result>
Doug, who runs track for his high school,
was challenged to a race by his younger
brother, Matt. Matt started running first,
and Doug didn’t start running until Matt
had finished a quarter-mile lap on the
school track. Doug passed Matt as they
both finished their sixth lap. If both boys
ran at a constant speed, with Doug running
2 miles an hour faster than Matt, what was
Matt’s speed?