75 miles per hour 

While going to the destination, the vehicle travels 10 mils
at the speed of 50 miles per hour. So the time taken to
travel 10 miles is 

= (60 * 10) / 50 

= 12 minutes 

Now it's given that round-trip travel time is 20 minutes. So
the vehicle should complete its return trip of 10 miles in 8
minutes. So the speed of the vehicle must 

= (60 * 10) / 8 

= 75 miles per hour