Michael and his sister Jane left their house at the same time going in the opposite direction. Michael drove at an average speed of
40 mph, while Jane drove at an average speed of 35 mph. After how many hours were they 400 miles apart?
Michael's distance --- x
Jan'e distance ---- 400-x
x/40 = (400-x)/35
35x = 16000 - 40x
solve for x, the distance that Michael went
divide x by 40 to get the time,
(check by dividing 400-x by 35, you must get the same answer)
d1 + d2 = 400.
40*T + 35*T = 400,
T = 5 1/3 Hours.
To find the number of hours it takes for Michael and Jane to be 400 miles apart, we can use the formula:
Distance = Speed * Time
Since they are driving in opposite directions, the total distance between them will increase at a rate equal to the sum of their speeds:
Total Distance = Michael's Distance + Jane's Distance
Since Michael is driving at 40 mph and Jane is driving at 35 mph, we can set up the equation:
Total Distance = (40 mph * Time) + (35 mph * Time)
Since the total distance is given as 400 miles, the equation becomes:
400 miles = (40 mph * Time) + (35 mph * Time)
Now we can solve for the time it takes for them to be 400 miles apart:
400 miles = (40 mph + 35 mph) * Time
400 miles = 75 mph * Time
Dividing both sides by 75 mph, we get:
Time = 400 miles / 75 mph
Time = 5.33 hours
Therefore, Michael and Jane will be 400 miles apart after approximately 5.33 hours.