Martina leaves 9am bicycle rate of 24mi/h. 2 hours later, John, driving rate of 48mi/h what time John catch up

Answer 1

Martina travels 48 miles in 2 h
Relative speed of John to Martina is 24 miles / h
t = 48 / 24 h
t = 2 h
John will catch up after 2 h

Answer 2

M rate = 24mph M time = x
J rate = 48 mph J time = x-2

Because D = r * t

Then M distance = 24 * x and J distance = 48 (x-2)

When their distances traveled are = then John catches up

24 x = 48 (x-2)
24x = 48 x - 96
-24 x = -96
x = 4 hours

Since x was time in hours after 9 am, then the time is 1:00 pm

Answer 3

Philo's approach is right but the time he is measuring from is John's departure time, so the answer is 1PM, two hours after John leaves and four hours after Martine leaves.

Do you really think Martina can keep up a pace of 24 mi/hr for 4 hours? Doesn't she need a break? or is this all down hill?

Answer 4

Martina's time is 2 hrs more than John's, so
distance(M) = distance(J)
rate * time = rate * time
24(t + 2) = 48t
24t + 48 = 48t
48 = 24t
t = 2 hr.

Answer 5

1pm

@11am Martina has covered 24*2 miles = 48 miles
@11am John leaves
@12pm Martina has cover 72 mile while John has covered 48
@1pm Martina has covered a total of 96miles while John has now covered 96 miles...

Answer 6

48 + 24t = 48t where t is in hours

48t - 24t = 48

24t = 48

t = 48/24 = 2

John will catch up after 2 hours, i.e. at 1 PM, after a distance of 96 miles.

Answer 7

48 + 24x = 48x
48 = 24x
x = 2
They meet 2 hours after John starts out, so 1 pm.

Answer 8

Yeah John, I thought that was one heck of a fit girl. 24mph on a bicycle? WOW!!! Even for short periods and downhill that's good going.