Anne left 10mins ago and you know she drives 60mi/hr. If you drive 70mi/hr how long will it take to get to her? how would i solve this problem?

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

The wording of this question is somewhat ambiguous. Suppose Anne left 10 minutes ago and stopped. (Lets say she calls you because she has a flat tire)

To find out how long it would take to get to her:

The distance Anne drove was `d=r*t=60"miles"/"hour"*(1/6)"hour"=10` miles.

To find the time to cover 10 miles at 70mph:

`10=70*t==>t=1/7` hours or a little over 8.5 minutes.

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

Let `t` be the time that you drive in minutes. When you catch up with Anne you will have both driven the same distance.

The distance you drove will have been `d=70t`

The distance Anne will have driven is `d=60(t+10)` -- she drove for 10 more minutes then you did.

Setting the expressions for the distance equal to one another:

`70t=60(t+10)`

`70t=60t+600`

`10t=600`

`t=60`

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It will take you 1 hour (or 60 minutes) to catch up with Anne.

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** If you prefer, you can solve for `t` in hours:

Your distance : `d=70t`

Anne's distance: `d=60(t+1/6)` since 10 minutes is 1/6 of an hour

`70t=60(t+1/6)`

`10t=10`

`t=1` hour.

The graph; distance is along the vertical axis in miles, time along the horizontal axis in hours:

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