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
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