let

v1 = the speed of Larry

d1 = 371 miles the distance Larry traveled

t1 = the time of Larry's travel

v2 = the speed of Terrell

d2 = 220 miles the distance Terrell traveled

t2 = the time of Terrel's travel

Larry's time to travel 371 miles is 3 hours more than Terrell's time to travel 220 miles

t1 = 3 + t2

Terrell drove 2 miles per hour faster than Larry

v2 = 2 + v1

we also know that speed = distance/time => time = distance/speed

t1 = d1/v1 = 371/v1

t2 = d2/v2 = 220/v2

plugin this values in t1 = 3 + t2 we get

371/v1 = 3 + 220/v2 multiply both sides by v1v2

371v2 = 3v1v2 + 220v1

and replace v2 = 2 + v1 in the above equations

371(2 + v1) = 3v1(2 + v1) + 220v1

solving the quadratic equation

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we find and consider only the positive roots since v1 > 0

v1 = 53 mph

v2 = 2 + v1 = 2 + 53 = 55

v2 = 55 mph

Larry traveled with 53 mph while Terrell traveled with 55 mph.