Question 117631
Rate x Time = Distance
Distance = Rate/Time
Let's call Bus Time and Bus Distance, T1 and D1.
Let's call walk time and walk distance, T2 and D2.
1.{{{D1+D2=22}}} Total distance is 22 miles.
2.{{{T1+T2=3}}} Total time is 3 hours.
3.{{{D1/T1=40}}} Rate of the bus is 40 mph.
4.{{{D2/T2=3}}} Rate of the accountant walking is 3 mph.
From 3,
3.{{{D1/T1=40}}}
{{{D1=40T1}}}
and from 4,
4.{{{D2/T2=3}}}
{{{D2=3T2}}}
You can substitute these values into 1.
1.{{{D1+D2=22}}}
{{{40T1+3T2=22}}}
{{{3T2=22-40T1}}}
{{{T2=(22-40T1)/3}}}
You can substitute this value for T2 into equation 2 and solve for T1.
2.{{{T1+T2=3}}}
{{{T1+(22-40T1)/3=3}}}
{{{3T1+22-40T1=9}}}
{{{22-37T1=9}}}
{{{-37T1=-13}}}
{{{T1=13/37}}}
From 2,
{{{T1+T2=3}}}
{{{13/37+T2=3}}}
{{{T2=3-14/37}}}
{{{T2=111/37-13/37}}}
{{{T2=98/37}}}
From 3,
{{{D1=40T1}}}
{{{D1=40(13/37)}}}
{{{D1=520/37}}}
From 4,
{{{D2=3T2}}}
{{{D2=3(98/37)}}}
{{{D2=294/37}}}
So in approximate terms, the accountant rides the bus 14.1 miles for 0.35 hrs(21 minutes).
Then walks 2.65 hrs (2 hrs, 39 minutes) for a distance of 7.9 miles.
Total distance is 14.1+7.9 or 22 miles.
Total time is 0.35+2.65 or 3 hours.