If you walk for 1.5 hours at 3 mph, how fast should you run during the next 0.5 hours to have the average speed of 4 mph?

Rate * Time  =  Distance

So

4 mph * 2 hrs  =  8  miles  to cover

And the toal distance covered in the first 1.5 hrs.  =  3 * 1.5  = 4.5 miles

So....in the last   .5 hrs....you must cover  8  - 4.5 miles  =  3.5 miles

So.....the rate in the last .5 hrs must be

Distance / Time  = Rate =  3.5 / .5  =    7 mph