How far does the person travel in km?

[runner1738]

A person takes a trip, driving with a constant speed 90.5 km/h except for a 15 min rest stop. If the person's average speed is 60.8 km/h, how much time is spent on the trip? Answer in units of h.

how far does the person travel? answer in units of km.

 

[MathStudent]

any ideas?? what are your thoughts so far??

What is the definition of average speed?

 

[runner1738]

average speed=total d/total t

 

[runner1738]

so what are you saying you use constant speed and average speed to get time traveled?

 

[MathStudent]

You're given ave speed, so if you you can find the distance traveled, then you can find the total time of the trip... using the equation

S_{ave} = \frac{d}{t}

Can you come up with an equation for the distance traveled that involves the total time?

 

[runner1738]

but we are supposed to use the total time to find the distance traveled though, so the only thing we can use is the difference between the constant speed and average speed and find time that way

 

[MathStudent]

The question asks for both the time and distance traveled... once one is solved, the other easily follows.

You have an equation with two unknowns, t and d... but your also given some other info... can you use that info to write one of the unknowns in terms of the other?

 

[runner1738]

i was thinking it was 60.8/90.5 gives you how long it takes him to go 60.8 km, then i got a decimal x 60 got minutes added 15, then went back to decimal and got .9218232044 which is around 55 min, but it wasnt right, what's wrong with this thinking?

 

[runner1738]

we know that 60.8= d/t, and 90.5t=d (constant acceleration means 0 velocity as well unless change in direction

 

[runner1738]

i just tried 90.5(t+.25)=60.8 because time + 15 min X the constant should equal the average right?

 

[MathStudent]

i just tried 90.5(t+.25)=60.8 because time + 15 min X the constant should equal the average right?

Any distance you cover is traveled at a speed of 90.5 km/h. So if t is the total time, then the part of that time spent moving is t - .25 hours. So if you multiply the speed your traveling by this time, you get the distance traveled, that is
d = 90.5(t - .25)

can you figure out the rest?

 

[runner1738]

yea i got it total time was .7165, and distance was 46.38125

 

[MathStudent]

good! my answer for time was 0.762 h, but I didn't round until the end so the differences can be explained by round-off error.. the distance is the same