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# During a trip, Francine traveled x percent of the total distance at an

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Director
Joined: 09 Mar 2016
Posts: 601
Re: During a trip, Francine traveled x percent of the total distance at an [#permalink]

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30 Dec 2017, 13:23
Thanks SO much niks18 for a fantastic explanation! Everything is clear! Highly appreciated !
Intern
Joined: 17 Jul 2016
Posts: 35
Re: During a trip, Francine traveled x percent of the total distance at an [#permalink]

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08 Jan 2018, 18:54
rate * time = distance

40_____ x/40_______________ = x

60_____ (100-x)/60_________ = 100-x

(100)/(x/40+[100-x]/60)

after simplifying we get choice E.

A good idea is to assume the distance is 100.
Director
Joined: 09 Mar 2016
Posts: 601
Re: During a trip, Francine traveled x percent of the total distance at an [#permalink]

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18 Apr 2018, 14:17
Bunuel wrote:
hardnstrong wrote:
Where does it say that total distance is 40 :
Distance is given as x % of total distance
we only have speed, which is 40m/ph and 60m/ph

Nowhere it's said that the total distance is 40 miles. I should have written this more clearly: distance $$d$$ will cancel out from the equation (edited the earlier post to clear this). So we can assume distance to be some number. I chose 40 as it's easy for calculation.

The solution with $$d$$:

$$Average \ speed=\frac{distance}{total \ time}$$.

Francine traveled $$x$$ percent of the total distance at an average speed of 40 miles per hour --> time needed for this part of the trip: $$t_1= \frac{distance_1}{speed_1}=\frac{\frac{x}{100}*d}{40}=\frac{dx}{40*100}$$;

Timed needed for the rest of the trip: $$t_2= \frac{distance_2}{speed_2}=\frac{(1-\frac{x}{100})*d}{60}=\frac{(100-x)d}{60*100}$$;

$$Total \ time=t_1+t_2=\frac{dx}{40*100}+\frac{(100-x)d}{60*100}=\frac{d(x+200)}{12000}$$;

$$Average \ speed=\frac{distance}{total \ time}=\frac{d}{\frac{d(x+200)}{12000}}=\frac{12000}{x+200}$$.

Hope it's clear.

Hi Bunuel

can you expain step by step(with comments) how from adding up two TIMES you get this $$\frac{d(x+200)}{12000}$$

$$Total \ time=t_1+t_2=\frac{dx}{40*100}+\frac{(100-x)d}{60*100}=\frac{d(x+200)}{12000}$$;

thank you

D.
Re: During a trip, Francine traveled x percent of the total distance at an   [#permalink] 18 Apr 2018, 14:17

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