Two groups of friends are taking taxis to a party in Yardley. The first taxi leaves from the financial district and travels at $33$ miles per hour. At the same time, the other taxi leaves from the marina and travels $45$ miles per hour. The two taxis are $5$ miles apart and heading directly toward each other. How much time will it take for the taxis meet? $\newline$ If necessary, round your answer to the nearest minute. $\newline$ hours and minutes

Full solution

Q. Two groups of friends are taking taxis to a party in Yardley. The first taxi leaves from the financial district and travels at

33

miles per hour. At the same time, the other taxi leaves from the marina and travels

45

miles per hour. The two taxis are

5

miles apart and heading directly toward each other. How much time will it take for the taxis meet?

\newline

If necessary, round your answer to the nearest minute.

\newline

____ hours and ____ minutes

Calculate combined speed: Calculate the combined speed of the two taxis. $\newline$ Speed of first taxi: $33$ miles per hour $\newline$ Speed of second taxi: $45$ miles per hour $\newline$ Combined speed $=$ Speed of first taxi $+$ Speed of second taxi $\newline$ Combined speed $= 33 + 45$ $\newline$ Combined speed $= 78$ miles per hour
Calculate meeting time: Calculate the time it will take for the taxis to meet. $\newline$ Distance between the taxis: $5$ miles $\newline$ Combined speed of the taxis: $78$ miles per hour $\newline$ Time $=$ Distance $/$ Speed $\newline$ Time $=$ $5$ miles $/$ $78$ miles per hour $\newline$ Time $hickapprox 0.0641$ hours
Convert time to minutes: Convert the time from hours to minutes. $\newline$ Time in hours: $0.0641$ hours $\newline$ Minutes in an hour: $60$ $\newline$ Time in minutes = Time in hours $\times$ Minutes in an hour $\newline$ Time in minutes = $0.0641 \times 60$ $\newline$ Time in minutes $\approx 3.846$ minutes $\newline$ Since we need to round to the nearest minute, the time is approximately $4$ minutes.