How long does Nicole need to drive before they are 240.9 mi. apart?

Question

Mike left school and drove toward the
ocean at an average speed of 25.5 mph.
Nicole left 0.6 hours later and drove in the
opposite direction with an average speed
of 45 mph. 

Answer 1

Remember that distance = rate × time. We'll write two equations: one for Mike and one for Nicole.

 

 

 

MIKE

 

We're not told how far Mike drove, so call that distance d. Mike drove at a rate of 25.5 MPH. We're not told how long Mike drove, so call that time t. So:

 

d = 25.5t

 

 

 

NICOLE

 

We're not told how far Nicole drove, but we know that together the two must drive 240.9 miles. So, Nicole must drive (240.9 - d) miles. Nicole drove at a rate of 45 MPH. We're not told how long Nicole drove, but we know she left 0.6 hours after Mike, so call that time (t - 0.6). So:

 

240.9 - d = 45(t - 0.6)

 

 

 

Now you have a system of equations:

 

d = 25.5t

240.9 - d = 45(t - 0.6)

 

Solve the second equation for d, then substitute that into the first equation to solve for t:

 

240.9 = d + 45(t - 0.6)

240.9 - 45(t - 0.6) = d

 

240.9 - 45(t - 0.6) = 25.5t

240.9 - 45t + 27 = 25.5t

267.9 - 45t = 25.5t

267.9 = 70.5t

3.8 = t

 

So, Mike drove for t = 3.8 hours before they were 240.9 miles apart. But we want to know how long Nicole drove. So...

 

3.8 - 0.6 = 3.2 hours