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Average speed problem
By Mick Chudasama (P2686) on Monday, August 14, 2000 - 09:44 pm:

Karen drives 210 miles in 4 hours. Her average speed is 60 mph for part of the time and 40 mph for the rest. For how long is her averge speed 60 mph?

Thanks.

By Anonymous on Monday, August 14, 2000 - 09:55 pm:

210 = 60T + 40t
4 = T + t

T is 2 1/2 hours
t is 1 1/2 hours

her average speed is 60mph for 2 1/2 hours.

By Mick Chudasama (P2686) on Monday, August 14, 2000 - 10:00 pm:

How did you work it out?

By Brad Rodgers (P1930) on Monday, August 14, 2000 - 10:27 pm:

We know that distance equals rate (speed) times time. Let's label distance as D.

We also know that the distance traveled is thus

(60miles/hour)(time taken at 60mph: call this T)

while traveling at an average of 60mph. Likewise the distance traveled at 40mph is

40mph(time taken at 40mph:call this t)

so the total distance, D, is

D=210=60T+40t

We are also given that the total time taken is 4

So,

4=T+t

That is the exact same pair of equations that the person above gave. See if you can figure out how to solve this system. If not just post again.

Brad

By Mick Chudasama (P2686) on Tuesday, August 15, 2000 - 12:06 am:

How did he get 2 1/2 hours for average speed at 60 mph?

By Brad Rodgers (P1930) on Tuesday, August 15, 2000 - 02:16 am:

Here are the steps:

Find that 4-T=t.

Substitute 4-T in for t in the equation:

210=60T+40t

(this may be simplified to 21=6T+4t, but doesn't have to be)

Solve for T.


Brad

By Michael Brame (T3019) on Tuesday, August 15, 2000 - 03:27 am:

One good way of solving problems like this is to draw a picture or diagram. Draw a line and label it 210 miles and 4 hours. Above that line draw an arrow with the tail even with the end of the line and label the arrow 60 mi/hr (miles per hour). Draw another arrow with the tail starting at the head of the first arrow and label it 40 mi/hr. The head of this arrow ends at the end of the line.

Some amount of time (T) passed while Karen had a velocity (speed) of 60 mi/hr. The total time that passed is 4 hr, so the time that passed while Karen had a speed of 40 mi/hr is (4-T)hr.
Since the total distance is 210 mi, the distance travelled at 60 mi/hr plus the distance at 40 mi/hr equals 210 mi. Distance travelled is equal to speed times the time;.
Gathering together this information, we have red distance (60 mi/hr)(T)hr + blue distance (40 mi/hr)(4-T)hr = 210 mi
60T + 40(4-T) = 210
60T + 160 - 40T = 210
20T = 50
T = 50/20 = 2.5 hr