Question

Frank started out in his car travelling 45 mph. When Frank was 1/3 miles away, Daniel started out from the same point at 50 mph to catch up with Frank. How long will it take Daniel to catch up with Frank

Answer 1

`Daniel\ will\ catch\ Frank\ in\ 4\ minutes.`

Explanation:

Let total distance
`=d`

Speed of Frank
`=45\ mph`

`Time\ taken\ to\ cover\ (1)/(3)\ miles=(distance)/(speed)=((1)/(3))/(45)=(1)/(135)\\\\Let\ after\ t\ hours(Daniel\ starts)\ Daniel\ will\ catch\ Frank.\\\\\\After\ t\ hours\ distance\ covered\ by\ Daniel=speed* times=50* t=50t\\\\Time\ taken\ by\ Frank=t+(1)/(135)\\\\Distance\ covered\ by\ Frank==speed* times=45* (t+(1)/(135))=45t+(1)/(3)\\\\Both\ the\ distance\ are\ equal\\\\Hence\ 50t=45t+(1)/(3)\\\\50t-45t=(1)/(3)\\\\5t=(1)/(3)`

`t=(1)/(15)\ hours\\\\t=(1)/(15)* 60\ minutes\\\\t=4\ minutes`