# physical science

A person takes a trip, driving with a constant speed 85.6 km/h except for a 22.6 minute rest stop.
If the person's average speed is 61.6 km/h, how far is the trip? Answer in units of km.

1. 👍
2. 👎
3. 👁
1. Let T be the total time (in hours) and X be the distance (in km). 22.6 minutes is 0.3767 hours. You can write two equations in the two unknowns:
X = 61.6 T (using the average speed)
and
X = 85.6 (T-.03767)
(using the time spent actually driving)
This means that
61.6 T = 85.6 T - 32.24
24.0 T = 32.24
T = 1.343 h
Now solve for X
X = ?

1. 👍
2. 👎
2. 22.6 minutes is 22.6/60 hours = 0.3737 hours

If for simplicity we take the rest stop at the start the total journey time is (0.3767 + t)
where t is the driving time.

If d is the distance travelled then speed =
d/t=85.6 km/h

However the average speed is from time zero, thus speed from time zero

is d/(t+0.3767)=61.6 km/h

Next step is to rearrange
d/t=85.6 km/h
with t as the subject and substitute in

d/(t+0.3767)=61.6 km/h

and solve for d

Hope this is OK.

1. 👍
2. 👎

## Similar Questions

1. ### physics

A person walks first at a constant speed of 4.90 m/s along a straight line from point A to point B and then back along the line from B to A at a constant speed of 2.70 m/s. (a) What is her average speed over the entire trip?

2. ### Physics

Anna is driving from Champaign to Indianapolis on I-74. She passes the Prospect Ave. exit at noon and maintains a constant speed of 75 mph for the entire trip. Chuck is driving in the opposite direction. He passes the Brownsburg,

3. ### math

A boat travels from one port A to port B, travelling 126 km, upstream (against the current) at a uniform speed, and the trip takes 6 hours. On the way back (downstream), the trip only takes 4.5 hours. Set up and solve a system of

4. ### Physics

A jet takes off from SFO (San Francisco, CA) and flies to YUL (Montréal, Quebec). The distance between the airports is 4100 km. After a 0.81-h layover, the jet returns to San Francisco. The total time for the round-trip

1. ### algebra

A man flies a small airplane from Fargo to Bismarck, North Dakota --- a distance of 180 miles. Because he is flying into a head wind, the trip takes him 2 hours. On the way back, the wind is still blowing at the same speed, so the

2. ### physics

A person walks first at a constant speed of 4.90 m/s along a straight line from point A to point B and then back along the line from B to A at a constant speed of 2.70 m/s. (a) What is her average speed over the entire trip?

3. ### Physics

A person initially at rest throws a ball upward at an angle θ0= 75 ∘ with an initial speed v0=15 m/s . He tries to catch up to the ball by accelerating with a constant acceleration a for a time interval of 1.03 s and then

4. ### physics

A person takes a trip, driving with a constant speed of 99.5 km/h, except for a 24.0-min rest stop. The person's average speed is 66.4 km/h. how far does the person travel?

1. ### algebra

8. A person starts at a position of 25 meters and finishes at a position of 2 meters. The trip takes 4.5 seconds. What is the person's average velocity? What is the person’s average speed? 9. A person starts at a position of 2

2. ### physics

a person walks first a constant speed of 5.00m/s along a straight line from point A to point B and then back along the line from point B to A at a constant speed of 3.00m/s. (a) what is her average speed over the entire trip? (b)

3. ### Math

When Sarah takes the bus to work, the trip takes 30 minutes. When she takes the train to work, the trip takes 20 minutes. The average speed to the train is 15 mph faster than the speed of the bus. Find the distance to work.

4. ### physics

A person walks first at a constant speed of 5.10 m/s along a straight line from point circled A to point circled B and then back along the line from circled B to circled A at a constant speed of 3.15 m/s.(a) What is her average