Question

Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 250 miles in the same time that Dana

Answer 1

Answer:

Chuck's speed is  37  mi/h .

Step-by-step explanation:

We're asked to find the speed, Chuck, with some given information.

To do this, let's first recognize the simplified velocity equation:

speed = distance/time

or,  rearranging to solve for time:

time = distance/speed

let's write this using symbols to simplify things:

time = s/v

s= distance

v= velocity

we're given that

1. s Chuck = 185  mi

2. sDana= 160 mi

3. vDana= x

4. vChuck= x+5

Let's plug these values in for two separate equations for each person:

Chick: t = 185/x+5

Dana: t = 160 mi/x

We're asked to find Chuck's speed given that the time intervals are equal, so what we can do is set these two equations (which are solved for the time,t ), equal to each other:

chuck             Dana

$\frac{185 mi}{x+5}$               $\frac{160 mi}{x}$

Now, we solve for x (which would be Dana's speed):  

Cross-multiply:

185x= 160(x+5)

distribute :

185x= 160z+800

subtract 160x from both sides:

25x=800

divide both sides by 25:

x=32 mi/h

Remember that Chuck's speed is:

v Chuck = x + 5

so

vChuck = 32mi/h+5mi/h= 37 mi/h