# Quadratic Equation application with distance , rate , and time .

• Oct 11th 2010, 05:45 PM
Kyrie
Quadratic Equation application with distance , rate , and time .
Naoki bikes the 36 mi to Hillsboro averaging a certain speed. The return trip is made at a speed 3 mph slower. Total time for the round trip is 7 hr. Find Naoki's average speed on each part of the trip.

I set up a table.

Trip 1: Distance = 36 Speed = r Time = ???
Trip 2: Distance = 36 Speed = r-3 Time = ???

What do I set time as? x divided by 7? $\displaystyle \frac{X}{7}$ ?
• Oct 11th 2010, 06:04 PM
harish21
for the first trip, if you suppose that he is travelling at a speed of x miles/hour and suppose that he takes t hours to complete the trip, then:
x miles/hour * t hours = 36

xt=36

likewise for the second trip, his speed is (x-3) miles/hour and time is (7-t) hours...
• Oct 11th 2010, 08:09 PM
Aurum
Quote:

Originally Posted by Kyrie
Naoki bikes the 36 mi to Hillsboro averaging a certain speed. The return trip is made at a speed 3 mph slower. Total time for the round trip is 7 hr. Find Naoki's average speed on each part of the trip.

I set up a table.

Trip 1: Distance = 36 Speed = r Time = ???
Trip 2: Distance = 36 Speed = r-3 Time = ???

What do I set time as? x divided by 7? $\displaystyle \frac{X}{7}$ ?

The easiest way to figure out what you should set t as is by using the equation for average speed, r=$\displaystyle \frac{d}{t}$. Solving for time multiply by t and then divide by speed so t=$\displaystyle \frac{d}{r}$.

Next Substitute in our given values for trip 1 and trip 2.
Trip 1: t=$\displaystyle \frac{36}{r}$
Trip 2: t=$\displaystyle \frac{36}{r-3}$

Now since we are also given the time for a round trip is 7 hours, we can say Trip 1 + Trip 2= 7 hours, $\displaystyle t_{1}$ + $\displaystyle t_{2}$.

$\displaystyle \frac{36}{r}$+$\displaystyle \frac{36}{r-3}$=7

Now you can solve by multiplying by a least common divisor and solve for r to find the speed of the first trip and subtract 3 from that for Naoki's average speed on the return trip.