Emily rode x miles, from her home, at a speed of p miles per hour befo

Question

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) \(\frac{1.5pt−2.5x}{5p−1}\)

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}

newyork2012 · Answer

Let’s say Emily walked her motorbike for S miles

x/p + s/0.3 + (s+x)/1.5p = t

(1.5x+5sp+s+x)/1.5p = t

s(5p+1)=1.5pt-2.5x

s=(1.5pt-2.5x)/(5p+1)

D

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GMATWhizTeam · Answer

Solution 
 • Let us assume that Emily walked her motorcycle for w miles.
• So, the distance traveled(in miles) by Emily in the first half of the journey   = x + w 
 o Thus, total time taken(in hours) by Emily to cover the first half of the journey  = \frac{x}{p} +\frac{w}{0.3} = \frac{x}{p} + \frac{10w}{3}  
• Now, the distance traveled(in miles) by Emily in the second half of the journey  = x + w 
 o Speed of Emily(in miles per hour) in the second half of the journey  = \frac{3}{2}*p 
o Thus, total time taken(in hours) by Emily to cover the second half of the journey  = \frac{(x+w)}{\frac{3}{2}p}  
• So, total time taken(in hours) by complete journey  = t = \frac{x}{p }+ \frac{10w}{3} + \frac{(x+w)}{\frac{3}{2}p} 
 o Or,  \frac{5x}{3p} +w(\frac{10}{3} + \frac{2}{3p}) = t 
  ⟹w \frac{(10p+2)}{3p }= t – \frac{5x}{3p} 
  ⟹\frac{w(10p+2)}{3p} = \frac{(3pt – 5x)}{3p}  
  ⟹w= \frac{(3pt – 5x)}{ (10p+2)} 
  ⟹w= \frac{(1.5pt – 2.5x)}{ (5p+1)}   
Thus, the correct answer is  Option D.

Kinshook · Answer

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

IMO D

bumpbot · Answer

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Emily rode x miles, from her home, at a speed of p miles per hour befo

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Emily rode x miles, from her home, at a speed of p miles per hour befo

Prep Toolkit

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