SOLUTION: Ride the peaks. Smith bicycled 45 miles going east from
Durango, and Jones bicycled 70 miles. Jones averaged
5 miles per hour more than Smith, and his trip took one-half
hour lo
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-> SOLUTION: Ride the peaks. Smith bicycled 45 miles going east from
Durango, and Jones bicycled 70 miles. Jones averaged
5 miles per hour more than Smith, and his trip took one-half
hour lo
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Question 203472This question is from textbook
: Ride the peaks. Smith bicycled 45 miles going east from
Durango, and Jones bicycled 70 miles. Jones averaged
5 miles per hour more than Smith, and his trip took one-half
hour longer than Smith’s. How fast was each one traveling?
I am not sure if i am suppose to use the D=r*t.
I am confused on how to set it up.
I know that smith's distance is 45 miles
and Jones distance is 70 miles
I am confused on how to write the part where Johes goes 5 miles per hour more then Smith and took one half hour longer then smith. This question is from textbook
You can put this solution on YOUR website! Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles.
Jones averaged 5 miles per hour more than Smith,
and his trip took one-half hour longer than Smith’s.
How fast was each one traveling?
:
Let s = D's speed
then
(s+5) = J's speed
:
Write a time equation: Time =
:
Smith's time = Jones' time - .5 hrs = - .5
Multiply equation by s(s+5)
s(s+5)* = s(s+5)* - .5s(s+5)
Cancel out the denominators and you have:
45(s+5) = 70s - .5s^2 - 2.5s
:
45s + 225 = 70s - .5s^2 - 2.5s
arrange as a quadratic equation on the left
.5s^2 + 2.5s + 45s - 70s + 225 = 0
:
.5s^2 - 22.5s + 225 = 0
Multiply equation by 2, get rid of the decimals
s^2 - 45s + 450 = 0
Factors to:
(s - 15)(s - 30) = 0
Two good solutions
s = 15 mph is Smith's speed, then 20 mph is Jones' speed
and
s = 30 mph is Smith's speed, then 35 mph is Jones' speed
:
:
Check solutions, find the time for each trip
Smith: 45/15 = 3 hr
Jones: 70/20 = 3.5 hr
:
You can check the s=30 solution
