At 2:00 p.m. Jimmy leaves Detroit traveling 48 miles per hour. At 2:15 p.m. Melissa leaves Detroit by the same route at 56 miles per hour. At what time will Melissa overtake Jimmy?

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baxthum8 | High School Teacher | (Level 3) Associate Educator

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This is a distance = rate x time  or `d = rt.`

THe distance they travel is the same as they both leave from Detroit and travel the same path.  Therefore, when Melissa overtakes Jimmy they will have travelled the same distance.

Jimmy follows `d = 48t`

since he travels 48mph and t represents time travelled in minutes

Melissa follows  `d = 56(t-15)`

since she travels 56 mph and started 15 minutes after Jimmy's time.

As stated earlier, since the distances are equal we can say:

`48t = 56 (t - 15)` Now let's solve for `t` .

`48t = 56t - 840` Subtract 56t from both sides we get:

`-8t = -840` Divide both sides by -8.

`t = 105` Since I used (-15) t was expressed in minutes.

So they will meet 105 minutes after 2:00 PM.  which will be at 3:45 PM when Melissa overtakes Jimmy.

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