Algebra average

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Algebra average

Randy made a business trip of 195 miles.  He averaged 54 mph for the first part of the trip and 57 mph for the second part. If the trip took 3.5 hours, how long did he travel at each rate?
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Re: Algebra average

distance = rate x time

At 54 mph
d = 54t   {distance = rate x time}

At 57 mph
d = 57(3.5 - t)   {rate x time.....time is the total time (3.5) - the 54 mph time (t)}

54t + 57(3.5 - t) = 195   {combined distances equal 195}
54t + 199.5 - 57t = 195   {used distributive property}
-3t + 199.5 = 195   {combined like terms}
-3t = -4.5   {subtracted 199.5 from each side}
t = 1.5   {divided each side by -3}

time at 54 mph is 1.5 hours

3.5 - t   {time at 57 mph}
= 3.5 - 1.5   {substituted 1.5, in for t, into 3.5 - t}
= 2   {subtracted}

time at 57 mph is 2 hours

- Algebra House