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Re: Emily rode x miles, from her home, at a speed of p miles per hour befo [#permalink]
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rheam25
Emily rode x miles, from her home, at a speed of p miles per hour before running out of fuel. She then walked her motorcycle at 0.3 miles per hour, for few miles further before she met her friend. After that, Emily’s friend dropped her back home, driving along the same route at a speed that was 50% greater than Emily’s riding speed for the first x miles. If the total journey took t hours, how many miles did Emily walk her motorcycle?

A) \(\frac{3pt−5x}{12}\)

B)\(\frac{1.5pt+2.5x}{5p−1}\)

C)\(\frac{1.5pt+2.5x}{5p+1}\)

D)\(\frac{1.5pt−2.5x}{5p+1}\)

E) \(\frac{1.5pt−2.5x}{5p−1}\)


Given:
1. Emily rode x miles, from her home, at a speed of p miles per hour before running out of fuel.
2. She then walked her motorcycle at 0.3 miles per hour, for few miles further before she met her friend.
3. After that, Emily’s friend dropped her back home, driving along the same route at a speed that was 50% greater than Emily’s riding speed for the first x miles.

Asked: If the total journey took t hours, how many miles did Emily walk her motorcycle?

Let the number of miles Emily walked her motorcycle be k miles.


Speed ************ Miles ************TIme
p miles/hr******** x miles ***********x/p hr
.3 miles/hr ******* k miles *********** k/.3 hr
1.5p miles/hr ***** x+k miles ******** (x+k)/1.5p hr

x/p + k/.3 + (x+k/1.5p = t
Multiplying the equation by 1.5p

1.5x + 5kp + x + k = 1.5pt
2.5x + (5p + 1)k = 1.5 pt
k = (1.5pt - 2.5x)/(5p+1) miles

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Re: Emily rode x miles, from her home, at a speed of p miles per hour befo [#permalink]
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Re: Emily rode x miles, from her home, at a speed of p miles per hour befo [#permalink]
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