tom left at 3 pm and traveled north going 50 mph and bill left from the same position at 6 pm and traveled north going 85 mph at what distance traveled will they cross paths
+129630 Call the time that Tom traveled, x + 3 hrs
Call the time that Bill traveled, x hrs
And rate * time = distance traveled.....and when Bill catches Tom, they have traveled the same distance.....so....
50(x + 3) = 85x simplify
50x + 150 = 85x subtract 50x from both sides
150 = 35x divide both sides by 35
x = 150/35 hs = 30/7 hrs = the time Bill traveled
So.....the distance traveled by each when they cross paths =
85(30/7) = about 364.3 miles
Let the distance travelled by both=d
Let the time travelled by both=t
Then we have:
d=50t + 150, and
d=85t
solve the following system:
{d = 50 t+150 | (equation 1)
d = 85 t | (equation 2)
Express the system in standard form:
{d-50 t = 150 | (equation 1)
d-85 t = 0 | (equation 2)
Subtract equation 1 from equation 2:
{d-50 t = 150 | (equation 1)
0 d-35 t = -150 | (equation 2)
Divide equation 2 by -5:
{d-50 t = 150 | (equation 1)
0 d+7 t = 30 | (equation 2)
Divide equation 2 by 7:
{d-50 t = 150 | (equation 1)
0 d+t = 30/7 | (equation 2)
Add 50 × (equation 2) to equation 1:
{d+0 t = 2550/7 | (equation 1)
0 d+t = 30/7 | (equation 2)
Collect results:
Answer: | d = 2550/7 and t=30/7
