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sherxon
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Andy makes a trip to a forest on his bicycle and Bob does so on his 01 Jul 2021, 23:56
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75% (hard)

Question Stats:

67% (03:24) correct 33% (02:42) wrong based on 182 sessions

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Andy makes a trip to a forest on his bicycle, and Bob does so on his motorcycle. Bob covers one mile 4 minutes faster than Andy does. They both spent two hours on their respective trips. However, Bob covered 40 miles more distance than did Andy. How many miles did Andy cover during his trip?

A. 10
B. 15
C. 20
D. 30
E. 40
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C
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Andy makes a trip to a forest on his bicycle and Bob does so on his 02 Jul 2021, 02:04
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sherxon
Andy makes a trip to a forest on his bicycle, and Bob does so on his motorcycle. Bob covers one mile 4 minutes faster than Andy does. They both spent two hours on their respective trips. However, Bob covered 40 miles more distance than did Andy. How many miles did Andy cover during his trip?

A. 10
B. 15
C. 20
D. 30
E. 40
Show more


I. Use options

Start from the central value and depending on answer can move to lower or higher values.
So A covers 20, => speed = 20/2 or 10mph, that is 1 mile in 60/10 or 6 minutes.
B covers 60 => speed = 60/2 or 30mph , that is 1 mile in 60/30 or 2 minutes, meaning 4 minutes faster than A.
Fits in exactly.

II. Algebraic
Let the time taken per mile By A be x, so by B is x-4
Distance traveled by A in 2 hours = \(\frac{60}{x}*2\)
Distance traveled by B in 2 hours = \(\frac{60}{x-4}*2\)

Thus extra distance traveled by B in 2 hours = \(\frac{120}{x-4}-\frac{120}{x}=40\)

\(120x-120x+480=40x^2-160x…..x^2-4x-12=0\)
\(x^2-6x+2x-12=0….(x-6)(x+2)=0\)

So x is 6, and distance traveled by A=120/6=20


C
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Andy makes a trip to a forest on his bicycle and Bob does so on his 07 Aug 2021, 22:24
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chetan2u
sherxon
Andy makes a trip to a forest on his bicycle, and Bob does so on his motorcycle. Bob covers one mile 4 minutes faster than Andy does. They both spent two hours on their respective trips. However, Bob covered 40 miles more distance than did Andy. How many miles did Andy cover during his trip?

A. 10
B. 15
C. 20
D. 30
E. 40


I. Use options

Start from the central value and depending on answer can move to lower or higher values.
So A covers 20, => speed = 20/2 or 10mph, that is 1 mile in 60/10 or 6 minutes.
B covers 60 => speed = 60/2 or 30mph , that is 1 mile in 60/30 or 2 minutes, meaning 4 minutes faster than A.
Fits in exactly.

II. Algebraic
Let the time taken per mile By A be x, so by B is x-4
Distance traveled by A in 2 hours = \(\frac{60}{x}*2\)
Distance traveled by B in 2 hours = \(\frac{60}{x-4}*2\)

Thus extra distance traveled by B in 2 hours = \(\frac{120}{x-4}-\frac{120}{x}=40\)

\(120x-120x+480=40x^2-160x…..x^2-4x-12=0\)
\(x^2-6x+2x-12=0….(x-6)(x+2)=0\)

So x is 6, and distance traveled by A=120/6=20


C
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How you consider 60 while finding distance in algebric method(2nd option)??I can't understand

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chetan2u
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Andy makes a trip to a forest on his bicycle and Bob does so on his 07 Aug 2021, 23:56
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SHEHAB01
chetan2u
sherxon
Andy makes a trip to a forest on his bicycle, and Bob does so on his motorcycle. Bob covers one mile 4 minutes faster than Andy does. They both spent two hours on their respective trips. However, Bob covered 40 miles more distance than did Andy. How many miles did Andy cover during his trip?

A. 10
B. 15
C. 20
D. 30
E. 40


I. Use options

Start from the central value and depending on answer can move to lower or higher values.
So A covers 20, => speed = 20/2 or 10mph, that is 1 mile in 60/10 or 6 minutes.
B covers 60 => speed = 60/2 or 30mph , that is 1 mile in 60/30 or 2 minutes, meaning 4 minutes faster than A.
Fits in exactly.

II. Algebraic
Let the time taken per mile By A be x, so by B is x-4
Distance traveled by A in 2 hours = \(\frac{60}{x}*2\)
Distance traveled by B in 2 hours = \(\frac{60}{x-4}*2\)

Thus extra distance traveled by B in 2 hours = \(\frac{120}{x-4}-\frac{120}{x}=40\)

\(120x-120x+480=40x^2-160x…..x^2-4x-12=0\)
\(x^2-6x+2x-12=0….(x-6)(x+2)=0\)

So x is 6, and distance traveled by A=120/6=20


C


How you consider 60 while finding distance in algebric method(2nd option)??I can't understand

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Time taken to cover one mile is x minutes, so x/60 hours.
Speed = 1 mile per x/60 hr =1/(x/60)mph=60/x mph.
Thus in 2 hours, the distance will be speed *2=60/x *2
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Andy makes a trip to a forest on his bicycle and Bob does so on his 26 Jun 2026, 12:52
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let B covers 1 mile in t hrs so speed =1/t mph
so A covers 1 mile in (t+4/60) hrs so its speed=15/(15t+1)
both travel for two hrs. and distance of B=40+distance of A
i.e. 2*15/(15t+1) +40 = 1*2/t
on solving 300t^2 + 20t - 1=0
(30t+1)(10t-1)=0
t=1/10
distance covered by B=2/t=2*10=20 miles
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