## 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 u

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

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3 months 2022-02-16T11:49:37+00:00 1 Answer 0 views 0

$$Daniel\ will\ catch\ Frank\ in\ 4\ minutes.$$
Let total distance$$=d$$
Speed of Frank$$=45\ mph$$
$$Time\ taken\ to\ cover\ \frac{1}{3}\ miles=\frac{distance}{speed}=\frac{\frac{1}{3}}{45}=\frac{1}{135}\\\\Let\ after\ t\ hours(Daniel\ starts)\ Daniel\ will\ catch\ Frank.\\\\\\After\ t\ hours\ distance\ covered\ by\ Daniel=speed\times times=50\times t=50t\\\\Time\ taken\ by\ Frank=t+\frac{1}{135}\\\\Distance\ covered\ by\ Frank==speed\times times=45\times (t+\frac{1}{135})=45t+\frac{1}{3}\\\\Both\ the\ distance\ are\ equal\\\\Hence\ 50t=45t+\frac{1}{3}\\\\50t-45t=\frac{1}{3}\\\\5t=\frac{1}{3}$$
$$t=\frac{1}{15}\ hours\\\\t=\frac{1}{15}\times 60\ minutes\\\\t=4\ minutes$$