Question

Sal was tired of waiting for Amir to show up at their meeting place, so he started running at an average speed of 4.5 mph without him. Ten minutes later, Amir still had 0.25 of a mile to go before he reached the meeting place, but Sal was 0.75 of a mile beyond it. If Amir is running at a faster pace, 6.7 mph, to the nearest hundredth of an hour, after how much time will Amir catch up to Sal?

Answer 1

Let s and a represent the position of Sal and Amir respectively.

s=.75+4.5t and a=-.25+6.7t

When Sal catches Amir, s=a so we can say.

-.25+6.7t=.75+4.5t subtract 4.5t from both sides

-.25+2.2t=.75 add .25 to both sides

2.2t=1 divide both sides by 2.2

t=5/11 hours

t≈0.45 hours (to nearest hundredth of an hour)