A bike running at 80 km/h initially is slowed down to 60 km/h as soon as the fuel indicator touches the half level mark. It keeps running at this speed till it runs out of fuel, thereby covering a total distance of 640 km in 10 hours. If the bike consumes 2 litres of fuel per hour, what is the capacity (in litres) of the fuel tank of the bike?
(A) 16
(B) 20
(C) 32
(D) 40
(E) 56
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A bike running at 80 km/h initially is slowed down to
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nkmungila1
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GMATGuruNY
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I believe that the following reflects the intent of the problem:
This is a MIXTURE problem.
Two speeds (60mph and 80mph) are combined to form a mixture with an average speed of 64mph.
To determine how much time must be spent at each speed, we can use ALLIGATION.
Let S = the slower speed and F = the faster speed.
Step 1: Plot the 3 speeds on a number line, with S and F on the ends and the average speed for the whole trip in the middle.
S 60----------64------------80 F
Step 2: Calculate the distances between the values on the number line.
S 60----4----64----16-----80 F
Step 3: Determine the ratio of the two given speeds.
The ratio of S to F is equal to the RECIPROCAL of the values in red.
S:F = 14:6 = 8:2.
Implication:
Of the 10 hours of travel time, 8 hours are traveled at 60mph and 2 hours are traveled at 80mph.
Since 2 liters are consumed for every hour spent traveling at 60mph, the total amount of fuel consumed during the 8 hours traveled at 60mph = 2*8 = 16 liters.
Since the tank is half full when the bike begins to travel at 60mph, these 16 liters constitute half of the tank's capacity.
Thus, the capacity of the tank = 2*16 = 32 liters.
The correct answer is C.
Average speed for the whole trip = d/t = 640/10 = 64 miles per hour.nkmungila1 wrote:A bike running at 80 km/h initially is slowed down to 60 km/h as soon as the fuel indicator touches the half level mark. It keeps running at this speed till it runs out of fuel, thereby covering a total distance of 640 km in 10 hours. Traveling at the lower speed, the bike consumes 2 litres of fuel per hour. What is the capacity (in litres) of the fuel tank of the bike?
(A) 16
(B) 20
(C) 32
(D) 40
(E) 56
This is a MIXTURE problem.
Two speeds (60mph and 80mph) are combined to form a mixture with an average speed of 64mph.
To determine how much time must be spent at each speed, we can use ALLIGATION.
Let S = the slower speed and F = the faster speed.
Step 1: Plot the 3 speeds on a number line, with S and F on the ends and the average speed for the whole trip in the middle.
S 60----------64------------80 F
Step 2: Calculate the distances between the values on the number line.
S 60----4----64----16-----80 F
Step 3: Determine the ratio of the two given speeds.
The ratio of S to F is equal to the RECIPROCAL of the values in red.
S:F = 14:6 = 8:2.
Implication:
Of the 10 hours of travel time, 8 hours are traveled at 60mph and 2 hours are traveled at 80mph.
Since 2 liters are consumed for every hour spent traveling at 60mph, the total amount of fuel consumed during the 8 hours traveled at 60mph = 2*8 = 16 liters.
Since the tank is half full when the bike begins to travel at 60mph, these 16 liters constitute half of the tank's capacity.
Thus, the capacity of the tank = 2*16 = 32 liters.
The correct answer is C.
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Scott@TargetTestPrep
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We can let the time the bike runs at 80 km/h = h hours, and thus the number of hours the bike runs at 60 km/h = 10 - h hours and we can create the following equation:nkmungila1 wrote:A bike running at 80 km/h initially is slowed down to 60 km/h as soon as the fuel indicator touches the half level mark. It keeps running at this speed till it runs out of fuel, thereby covering a total distance of 640 km in 10 hours. If the bike consumes 2 litres of fuel per hour, what is the capacity (in litres) of the fuel tank of the bike?
(A) 16
(B) 20
(C) 32
(D) 40
(E) 56
80h + 60(10 - h) = 640
80h + 600 - 60h = 640
20h = 40
h = 2
Thus, the bike runs at 60 km/h for 10 - 2 = 8 hours, which will consume 8 x 2 = 16 litres of fuel since the bike consumes 2 litres of fuel per hour. Recall that the bike starts to run at 60 km/h when the fuel tank is half full, so the tank must have 32 litres of fuel when it's full.
Answer: C
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