Daniel drove a 880-mile distance in two days. In the first day, he dro

Question

Daniel drove a 880-mile distance in two days. In the first day, he drove a certain part of it and his car consumed 20 gallons of fuel. In the second day, he drove the remaining distance and his car consumed again 20 gallons of fuel. If the mileage (miles traveled per gallon) of his car in the second day was 20% greater than the mileage of his car in the first day, what was the mileage of Daniel’s car in the first day?

A. 35
B. 30
C. 25
D. 20
E. 15

A. 35
B. 30
C. 25
D. 20
E. 15

Sol- Total Distance=880 miles
 Total Fuel Consumed= 20+20= 40 gallons
 Mileage for 2 days= 880/40= 22 miles/gallon
 first and second day's mileage equals 22.
 if we take the mileage of first day as x, then second day's mileage would be-
 22-x= x+0.2x
 22-x=1.2x
 22=2.2x
 10=x (first day's mileage)

AndrewN · Answer

Hello,  Rohansaini1997 . To address your query, the first half of your solution is fine. All you need to do is keep your eye on the average. If the mileage of the first day is  x , then the mileage of the second day is 1.2 x . Then, you just have to set up an equation based on the information you have worked out:

\frac{x + 1.2x}{2}=22

x + 1.2x = 44

2.2x = 44

Here, I multiplied through by 10, since I find working with whole numbers much less likely to lead to errors.

x = 20

Perhaps the question makes more sense now. Good luck with your studies.

- Andrew

Kinshook · Answer

Given: Daniel drove a 880-mile distance in two days. In the first day, he drove a certain part of it and his car consumed 20 gallons of fuel. In the second day, he drove the remaining distance and his car consumed again 20 gallons of fuel.

Asked: If the mileage (miles traveled per gallon) of his car in the second day was 20% greater than the mileage of his car in the first day, what was the mileage of Daniel’s car in the first day?

Let the distance travelled on the first day be x miles
Distance travelled on second day = 880 - x miles

Mileage for first day = x/20 miles/gallons
Mileage for second day = (880-x)/20 miles/gallons

The mileage (miles traveled per gallon) of his car in the second day was 20% greater than the mileage of his car in the first day
1.2x/20 = (880-x)/20
1.2x = 880-x
2.2x = 880
x = 400 miles

Mileage on first day = 400/20 = 20 miles/gallons

IMO D

xiao1058 · Answer

I got Ans D.

Since the second day's rate (or miles per gallon) was 1.2 times the first day's rate, we can set up a matrix (r stands for rate in the matrix below).

Day Rate Time Distance

1st day r 20 gal 20r

2nd day 1.2r 20 gal 24r

Since total distance travelled is 880 miles and 20r+24r=44r, we can set these numbers equal to each other.

44r=880 
r=20

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Daniel drove a 880-mile distance in two days. In the first day, he dro

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