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

1. ## 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? $\frac{X}{7}$ ?

2. 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...

3. 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? $\frac{X}{7}$ ?
The easiest way to figure out what you should set t as is by using the equation for average speed, r= $\frac{d}{t}$. Solving for time multiply by t and then divide by speed so t= $\frac{d}{r}$.

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

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

$\frac{36}{r}$+ $\frac{36}{r-3}$=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.