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Relative speed = 10 mph

At 10.30 car A would have traveled 20 miles

If car B has to be 40 miles ahead of car A, then it has cover the above 20 miles and be ahead by 40 miles. i.e. Net additional distance car B has to cover = 60 miles

Time taken to complete 60 miles = 60/10 = 6 hours

Car B will be ahead of car A by 40 miles at 10.30 am + 6hrs = 4.30 pm

Answer: C
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Let X be the total distance traveled by CAR A in (T+0.5) - Starting Half Hour earlier.
= X=40(T+0.5)
Total distance traveled by CAR B in time T,
= X+ 40 = 50 T

Put Value of X from eq 1 in eq 2
= 40 (T+0.5) + 40 = 50 T
deriving
=T= 6 Hours

Starting at 10:30 AM, At 16:30 PM (6 Hours)

Hope it helps.
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A starts at 10:00 and by the time B starts A is 20 miles ahead
now B has to go 40 mile ahead, and b has to cover 20 miles also
so total 60 miles
50-40 = 10 miles/ hour relative seed ....
6 hours 10:30+6 = 4:30
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Bunuel
Car A and Car B are each traveling along the same stretch of highway in the same direction. Car A leaves at 10:00am traveling at a constant rate of 40 miles per hour and Car B leaves at 10:30am traveling at a constant rate of 50 miles per hour. At what time will Car B be 40 miles ahead of Car A?

A. 3:30pm
B. 4:00pm
C. 4:30pm
D. 5:00pm
E. 5:30pm

Bunuel

Could we simply do

40 +20/ (50-40) = 6

10:30 + 6 hours?
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Bunuel
Car A and Car B are each traveling along the same stretch of highway in the same direction. Car A leaves at 10:00am traveling at a constant rate of 40 miles per hour and Car B leaves at 10:30am traveling at a constant rate of 50 miles per hour. At what time will Car B be 40 miles ahead of Car A?

A. 3:30pm
B. 4:00pm
C. 4:30pm
D. 5:00pm
E. 5:30pm

Car A’s speed is 40 mph and it starts at 10:00 a.m., so when Car B starts at 10:30 a.m., Car B will be 40 x 1/2 = 20 miles behind Car A. To determine what time will Car B be 40 miles ahead of Car A, we can use the following formula:

change in distance/change in rate = time

The change in distance is 60 miles, since Car B needs to catch up to Car A starting from 20 miles behind and needing to be 40 miles ahead. The change in rate is 50 - 40 = 10 mph. Thus:

60/10 = 6 hours

So, Car B needs 6 hours to be 40 miles ahead of Car A. Since Car B starts at 10:30 a.m., it will be 40 miles ahead of Car A at 10:30 a.m. + 6 hours = 4:30 p.m.

Answer: C
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When car B starts its trip, it's already 20 miles behind. For it to be 40 miles ahead of A, 60 miles have to be "recovered".

Since car B is 10 mph faster than A, car B will take 6 hours to "recover" the 60 miles, which will be achieved at 4:30 pm.
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