At 3:00 pm, a car has driven 30 miles east. It will continue to drive

the car travels for 40 minutes @0.8 minutes per mile..
so it travels \(\frac{40}{0.8} = 50\)miles in 40 minutes..

these 50 miles include 30 miles that he has to cover one side...
so distance till he turns around =\(\frac{50-30}{2} = 10\)
A

At 3 pm a car is 30 miles east from its starting point. Now after travelling some distance x, let us say the car turns back. Now this car covers x+30 miles to reach starting point.

Now when this car reaches starting point the time is 3:40 PM.

This means that in 40 minutes, this car has travelled a distance of x +x + 30 Miles.

x miles the car is travelling further East

x+30 This car has turned and is travelling in opposite direction, i.e. West.


Total distance: 2x+30 miles.

Speed of car is given in convoluted form. 8 minutes per mile.

0.8 minute -------car covers ----------1 mile
In 1 minute ---this car will cover---- 1/0.8 mile = 1.25 miles.

Speed of car: 1.25 miles per minute

so \(\frac{2x+30}{1.25}\) = 40 minutes

2x+30 = 50

2x = 20.

x = 10 miles.
Answer: A

Distance covered by Car in .8 mins = 1 mile
distance covered by car in 1 min = 1/(.8) = 1/(4/5) = 5/4 = 1.25 mile

Car continues to drive east at 0.8 minutes per mile and then turn around and drive at 0.8 minutes per mile back to its original starting point .
Time needed by car to cover 30 miles that was driven before 3 pm = 30/(5/4) = 24 mins

Since car needs to arrive back to its original starting point by 3:40 pm , we have 16 mins of travel time left . This time needs to divided equally in travel time in opposite directions .
So , the car will travel 8 mins towards east and 8 mins towards west .

Distance car can drive before turning around = (5/4) * 8 = 10 miles
Answer A

Responding to a pm:

The question says: "At 3:00 pm, a car has driven 30 miles east."
This means the car has already driven 30 miles east (it uses present perfect tense "has driven" which means the action has just been completed).
It is at a point 30 miles east of its starting point.


S --------------(30 miles) --------------- P (at 3:00)


Now it has to travel further ahead and turn back and reach S by 3:40

S --------------(30 miles) --------------- P (at 3:00)------- (x) -------------->
(at 3:40) <-----------------------------(x + 30)-----------------------------

In 40 mins, it travels x + x + 30 miles.

Does this help?

Please follow below fig.

let x be the distance covered then in 8 minutes @ 0.8 minutes/mile distance covered = 8/0.8 = 10
Ans A

We are given that a car has driven 30 miles east and that it can drive for another 40 minutes or a total of 40/0.8 = 50 miles. Thus, the total number of miles driven is 30 + 50 = 80 miles. So, the car will have to turn around when it reaches 80/2 = 40 miles, and thus the car can drive for another 40 - 30 = 10 miles.

Answer: A

The car has a uniform speed, it travels 1 mile in .8 minutes
so for the last 30 miles it will take 30 * .8 = 24 minutes
So out of a total time of 40 minutes , 24 will be required for the last 30 miles .
So the car has a total 16 minutes to make the forward an return journey.
Which means the car only 8 minutes to travel forward.
we know the speed is 1 mile in .8 minutes , hence in 8 minutes the car will travel 10 miles.

Answer = 10

More elaborately :Let the starting point be S
From point S, a car has traveled 30 miles let this be point B, after which the time is now 3:00 PM, then it has a uniform speed of 1 mile in .8 minutes. The car has to travel forward till say point E then return to point B then continue back 30 miles to point S.

So from B ---E -----B----S the car has a total of 40 minutes . We know the distance from B to S = Distance from S to B hence 30 miles
So time taken for B to S= 24 minutes ( 30 * .8)
Hence only 16 minutes from B to E and E to B , or only 8 minutes one way .
A car taking .8 minutes to travel 1 mile , will travel 10 miles in 8 minutes.
Answer = 10.

For me, it's easier to visualize this question if i think about how many miles the car "is allowed" to travel in 40 minutes, given a rate of .8 minutes per mile. Since there are 60 seconds in a minute, we can do 40x60= 2400 total seconds available for travel. Now, let's find how many seconds it takes to travel to mile. Since the car travels at .8 minutes/mile, the seconds per mile can be found by simply multiplying 60x.8 = 48. So, we have 2400 seconds available, and are traveling at a rate of 48 seconds/mile. If we divide 2400/48 = 50, we can see that if the car is traveling at a rate of 48 seconds/mile, it can travel 50 miles in 2400 seconds. The car has already traveled 30 miles, and has additional 50 miles left. Therefore, the car can travel an extra 10 miles east, which leaves room to travel 40 minutes back to the starting point. 40 + 10 = 50. The car can travel an additional 10 miles.

A

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