Rational Equations

Question

Two groups of friends are taking taxis to a party in Greenville. The first taxi leaves from the financial district and travels at 45 km/h. At the same time, the other taxi leaves from the marina and travels 62 km/h. The two taxis are 14 km apart and heading directly towards each other. How much time will it take for the taxis to meet? If necessary, round your answer to the nearest minute. Show All Work.

Answer 1

Hi Jacob.

It may be easier to think of this as 2 different Distance problems that are equal to each other. In both cases we know the Rate (45 in one, 62 in the other) and the Distance is the same for both (14)

Since both are moving directly towards each other, the combined Rate at which they are covering the Distance is the two Rates combined, 45+62. It's just as if it were a single vehicle traveling 107 kph to cover the distance.

So using our Distance formula D=RT, we have 14=107T.

Divide both sides by 107 14/107=107T/107

And we have the Time in hours 0.13 hours

Multiply by 60 to get Time in minutes 7.85 minutes

Hope this helps.

michael.russell.10

Answer 2

Since the two taxis travel the same amount of time t,

(45+62)t=14 and t=14/107 hr...you do the arithmetic to get minutes!