Question 7335
Using {{{d = rt}}} as a basis and since the time, t, is the same for both travellers. you can set up the proportion as follows:

{{{d1/r1 = d2/r2}}} Where: d1 = 270 miles, d2 = 330 miles, r1 is Leon's speed and r2 is Pat's speed.

But, Pat's speed (r2) is 10 mph more than Leon's speed.  So, r2 = r1 + 10

{{{270/r1 =  330/(r1+10)}}} Cross-multiply.

{{{270(r1+10) = 330(r1)}}} Simplify and solve for r1 (Leon's speed)

{{{270r1 + 2700 = 330r1}}} Subtract 270r1 from both sides.

{{{2700 = 60r1}}} Divide both sides by 60.

{{{45 = r1}}}  

Leon's speed is 45 mph.

Pat's speed is 45 mph + 10 mph = 55 mph.

Check:

The travel times should be the same for both travellers.

Leon's tims: {{{t1 = 270 miles/45 mph}}} = 6 hours

Pat's time: {{{t2 = 330 miles/55 mph}}} = 6 hours.