Question

Jessica and Myra just met up in Cedarburg for the afternoon, and now it is time for them to

get in their cars and head home. Jessica heads due east at 76 kilometers per hour, and Myra
heads due west at 87 kilometers per hour. How long will it be until they are 63 kilometers
apart?

Answer 1

0.3865 hours, or 23 minutes 11 seconds

Explanation:

You want the time it takes for separation distance to be 63 km if one car is headed east at 76 km/h, and one is headed west at 87 km/h.

Separation speed

The speed at which the cars are separating is the sum of their speeds in opposite directions:

76 km/h + 87 km/h = 163 km/h

Time

The relation between time, speed, and distance is ...

time = distance/speed

The time it takes for the separation distance to be 63 km is that distance divided by the separation speed:

time = (63 km)/(163 km/h) ≈ 0.3865 h

In minutes and seconds, this is about 23 minutes 11 seconds.

It will be about 0.3865 hours until they are 63 km apart, or 23 minutes 11 seconds.

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Additional comment

Numbers expressed as hours : minutes : seconds are effectively a base-60 notation. Similarly, degrees : minutes : seconds are also a base-60 notation system. The attached calculator shows the use of a →DMS function to convert hours to hours : minutes : seconds. This saves the effort of repeated division by 60 and keeping the remainder.