If Brittney drives to work, from home, at 50 mph, she’d arrive 1 minute late. If she drove at 60 mph, she’d arrive 5 minutes early.

Question

How far from work does Brittney live?

Answer 1

Hello, Michael,

Let's say D is the distance, T is time, and S is speed. I'll use T1 and S1 and T2 and S2 for the two scenarios where she is either late or early. Distance is the same for all cases.

D = T*S

D = T1*S1 and D = T2*S2

Now lets say time is equal to T + 1 for the late arrival (50mph), and time is equal to T-5 for the early arrival 60mph). so:

For the 50mph case, we have D = (T + 1)*50mph

and for 60 mph we have D = (T - 5)*60mph

Note that our time is set up as minutes, which the speed is mile per hour. We need to put them on the same time basis. I decided to convert the mph numbers into mile per minute (mpm) by dividing each speed by 60 min/hr. This gives:

and

Now we can make two equations and set them equal to each other, since both are equal to D, the distance.

Distance using the slow speed is D = 0.833(T + 1)

Distance using the higher speed is D = 1.00(T-5)

Set them equal to each other (D is the same) and solve for T. T is equal to 35.3 minutes.

Add 1 and/or subtract 5 from this time to get the actual times Britany spent driving. Use those times multiplied by the speed (in mpm) to get the actual mileage. I get around 35 miles.

I hope this helps,

Bob