Distance = rate x time

d = rt

**Motorcycle**rate = 40

time = t

d = 40t

**Car**rate = 60

time = 11 - t {total time was 11 hours}

d = 60(11 - t)

Total distance was 540. Add the distances and set equal to 540.

40t + 60(11 - t) = 540 {added distances and set equal to 540}

40t + 660 - 60t = 540 {used distributive property}

-20t + 660 = 540 {combined like terms}

-20t = -120 {subtracted 660 from each side}

t = 6 {divided each side by -20}

distance of motorcycle

d = 40t

= 40(6) {substituted 6, in for t, into motorcycle distance}

= 240 {multiplied}

**distance of motorcycle = 240 miles**- Algebra House

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