SOLUTION: please help me solve this word problem:
On the first past of a 317-mile trip, a salesperson averaged 58 miles per hour. he averaged only 52 miles per hour on the last part
Algebra ->
Customizable Word Problem Solvers
-> Travel
-> SOLUTION: please help me solve this word problem:
On the first past of a 317-mile trip, a salesperson averaged 58 miles per hour. he averaged only 52 miles per hour on the last part
Log On
Question 162377This question is from textbook Algebra and Trigonometry
: please help me solve this word problem:
On the first past of a 317-mile trip, a salesperson averaged 58 miles per hour. he averaged only 52 miles per hour on the last part of the trip because of an increased volume of traffic. the total time of the trip was 5 hours and 45 minutes. Find the amount of time at each of the two speed. This question is from textbook Algebra and Trigonometry
You can put this solution on YOUR website! What you can't do, and can never do, is take an average of
averages and get an average speed for the whole trip, in
other words, this never works (1st ave speed + 2nd ave speed)/2 = ave for total
You just can't do that.
Let = the distance traveled on the 1st part of trip
Let = the distance traveled on the 2nd part of the trip
Let = the time in hours for the 1st part
Let = the time in hours for the 2nd part
For the 1st part,
(1)
For the 2nd part,
(2)
Substitute in (1) for in (2) hrs
And,since is the time for the 2nd part, hrs
The 1st part of the trip took 3 hours
The 2nd part took 2 hrs and 45 min
check: Is the distance travelled on the 2nd part
OK
You can put this solution on YOUR website! let x = amount of time spent doing 58 miles per hour.
let y = amount of time spent doing 52 miles per hour.
-----
amount of time spent doing 58 miles an hour plus amount of time spent doing 52 miles per hour equals total number of miles.
-----
58*x + 52*y = 317
-----
total time spent is 5 hours 45 minutes which is the same as 5.75 hours since 45 minutes is 3/4 times 60 minutes = 3/4th of an hour = .75 of an hour.
-----
time spent doing 58 miles per hour plus time spent doing 52 miles an hour equals total time spent.
-----
x + y = 5.75
-----
you have 2 equations in 2 unknowns.
they are:
58*x + 52*y = 317
x + y = 5.75
-----
you can make x = 5.75 - y and substitute in other equation, or
you can solve these simultaneously by multiplying equation 2 by 58 and then subtracting one of the equations from the other one.
-----
solving as simultaneous equations works as follows:
multiply x+y equation by 58
2 equations become
58*x + 52*y = 317
58*x + 58*y = 58*5.75
-----
subtracting the second equation from the first gets
0*x + 52*y - 58*y = 317 - 58*5.75
-----
the x has been eliminated and you are left with
52*y - 58*y = 317 - 58*5.75
-----
multiplying out and combining like terms gets
-6*y = 317 - 333.5
which becomes
-6*y = -16.5
which becomes
-y = -2.75
multiplying both sides by -1 and it becomes
y = 2.75
-----
since y = 2.75, and x + y = 5.75, then x = 3.0
-----
you have
x = 3.0
y = 2.75
-----
substituting in 58*x + 52*y = 317 gets
58*3.0 + 52*2.75 = 317
which becomes
174 + 143 = 317
which becomes
317 = 317
-----
answer is
x = 3.0
y = 2.75
-----
if you did it the other way by taking x + y = 5.75 and solving for x, you would have gotten x = 5.75 - y.
substituting in the other equation for x, you would have gotten
58*(5.75-y) + 52*y = 317
and you would have arrived at the same answer.
-----
(