Bank robbers leave the bank with the bounty. the cops get alerted right away, but it takes them 4 minutes before they start in hot pursuit. the police station is 10 miles down the road from the bank in the direction opposite to that in which the robbers are heading. if the robbers travel at 96 mph how fast must the cops go to catch them before they reach the state line 55 miles away

In 4 minutes, 1/15 hour, the robbers have a (96 mi/h)·(1/15 h) = 6.4 mile head start.

The cops must travel 65 miles in the time the robbers travel 48.6 miles. Hence their speed must be 65/48.6 times that of the robbers, or about

... 65/48.6×96 mi/h ≈ 128.4 mi/h

The chase will be over after (55 mi)/(96 mi/h) = 34 minutes 22.5 seconds from the time of the robbery. The cops will have to cover the 65 miles in less than 30:22.5 minutes, or about 0.50625 hours.

The cops' speed then is 65 miles/(0.50625 hour) ≈ 128.39506... mi/h