A bus leaves at 9.00 am at 50 mph. At 1.00 pm a plane leaves at 300 mph.What time will the plane overtake bus?

Question

Both bus & plane travel in a straight line and in the same direction.

I need this for my homework assignment. Thanks.

Answer 1

This question needs more clarification, you see even at 300 m.p.h. an airplane needs to elevate which means there will be distance vertically about 2 minutes more than their estimates roughly a plane escalates vertically, not flat like a bus, but maybe the teacher wants their answer however incorrect it is.

Answer 2

Here's the easy way to think about it.

1) How far does the bus go before the plane starts?

Answer:  The bus travels for 4 hours at 50 mph.  So it goes 200 miles.

2) How long does it take for the plane to make up the 200 mile headstart?

Answer:  The plane is traveling 250 mph faster than the bus.  200 miles going at 250 mph --> 200/250 = 20/25 = 4/5 hour = 48/60 hours = 48 minutes

Answer:

48 minutes later at 1:48 pm

You can also do this in a slightly longer way:

Let t be the number of hours after 9am.

The distance the bus has traveled is 50t

The distance the plane has traveled is 300(t - 4)

You want the time when both have traveled the same distance, so equate these and solve for t:

300(t - 4) = 50t

300t - 1200 = 50t

250t - 1200 = 0

250t = 1200

t = 1200/250

t = 4.8

4.8 hours after 9am is:

4 hours 48 minutes

(0.8 = 8/10 = 48/60)

Answer:

1:48 pm

Answer 3

at 1:48

Answer 4

x = hours it takes for plane to catch up with bus

50(4 + x) = 300x

200 = 250x

x = 200/250

x = 0.8 hours or 48 minutes

Plane will overtake bus at anytime greater than 1:48

Check:

48/60hours * 300mph = 240miles

4.8hours * 50mph = 240miles

Answer 5

After 4 hours bus has travelled 200 miles

Consider bus to be now at rest and plane travelling at 250 mph

ie relative speed of plane to bus = 250 mph

t = 200 / 250 h

t = 0.8 h

t = 48 min

Will overtake at 1:48 pm

Answer 6

Let t be the period of time (from 1.00PM )needed for the plane to overtake the bus

50*4 + 50*t=300t

<=>t=0.8 hour

==> The plane will overtake the bus at 1.48 PM