Question

Emily takes a trip, driving with a constant velocity of 87.5 km/h to the north except for a 22 min rest stop. If Emily's average velocity is 76.8 km/h to the north, how long does the trip take?

Answer 1

Answer:

2.63 hours

Explanation:

First we have to read carefully the problem, It start telling us that Emily was driving with average velocity of 87.5 km/h to the north. Velocity is a physical variable that is definded in terms of :

• Speed of the object (87.5 km/h)

• Direction of the object (north)

Them the problem says that Emily's trip has an average velocity of 76.8 km/h to the north because she made a rest stop for 22 minutes.

Now you can ask yourself: If Emily was driving at 87.5 km/h, why the average speed of the trip was 76.8 km/h?

we need to see how speed is defined:

$Speed=\frac{distance}{time} =\frac{x}{y}$

***Note 1:

• Distance will be called as "x"  and units will be kilometers(km)

• Time will be called as "y" and units will be hours(h)

So,  87.5 km/h would be the average speed for a distance "x" and a time "y" without stops. But Emily made a stop that took 22 minutes. For the same distance Emily's trip took more time and time is in the denominator. If our numerator is constant and our denominator gets higher, the final result will be lower

Now, we have the follow expressions:

$87.5=\frac{x}{y}~~(1) \\76.8=\frac{x}{y+\frac{22}{60}}~~(2)$

***Note 2:

• we need to convert 22 minutes to hours. 1 hour= 60 minutes, so we need to apply the follow covert factor:

$y(hours)=y(minutes)*\frac{1(hour)}{60(minutes)}$

The problem aks us about how long does the trip take, it means that we have to find y.

We have two variables (x and y), and we have two equationts. We know that x have the same value for both problems (Because both average speeds have the same distance), so we can solve both equations for x and made equal each other

$87.5*y=x~(3)\\76.8*(y+\frac{22}{60})=x~(4)$

$87.5*y=76.8*(y+\frac{22}{60})~(5)$

We have to expand (5) and then we have to solve for y  

$87.5*y=76.8*y+76.8*\frac{22}{60}~~(6)\\87.5*y-76.8*y=76.8*\frac{22}{60}~~(7)\\10.7*y=76.8*\frac{22}{60}~~(8)\\y=\frac{76.8}{10.7}*\frac{22}{60}(hours)~~(9)\\y=2.63(hours)~~(10)$