Algebra Porblems Distance?
Show an equation and a solution for the problem. At noon a train leaves Bridgetown heading east at 90 mph to Cartertown. Another train leaves Bridgetown at 1:00 p.m. also heading east at 100 mph. In how many hours after the second train left will they pass each other?
Show an equation and a solution for the problem. A cargo plane left the San Francisco International Airport at noon, traveling east. At the same time, a jet left the Houston Airport traveling west 250 mph faster than the cargo plane. If the airports are 1,403 miles apart and the jet passes the cargo plane in 2.3 hours, what is the speed of each?
Comments
Like the last problem, set up your variables
Let v1 = Train1 speed
Let v2 = Train2 speed
distance = velocity * speed
**Since you want to find out when they pass, set they distances equal to each other, and solve for t.
distance(Train1) = v1*t
distance(Train2) = v2*t
time(Train1) = x + 1 (since it leaves an hour late)
time(Train2) = x
v2*t = v1*t
100*x = 90*(x + 1)
100x = 90x + 90
10x = 90
x = 9 hours
For this one set up your variables again first:
Let Cargo Speed = v
Let Jet Speed = v + 250
distance(Total) = 1403 mi
time = 2.3 hours
distance = velocity * time
distance(Total) = v * (2.3 hr) + (v + 250)*(2.3 hrs)
1403 mi = v * (2.3 hr) + (v + 250)*(2.3 hrs)
1403 mi = 2.3v + 2.3v + 575mi
828 mi = 4.6v
v = 180 mph = Cargo Speed
v + 250 = 430 mph = Jet Speed
1pm leaving train will cover a distance of 100t where t is the time in hours. Since the noon train has been in motion for an hour more, say 90(t+1) is the distance travelled. Set them equal to each other and you get 90t + 90 = 100t or 10t=90 or t=9 which means after 9 hours or at 10pm, both trains will be 900 miles east of Bridgetown.
Let the distance the cargo plane travels equal z and the distance the jet travels equals y. Well y + z = 1403
x is the speed of the cargo plane and x+250 is the speed of the jet. So, z= 2.3x and y = (x+250)* 2.3 or y = 2.3x+575 or y =z+575 and y = 1403 -z so combine them and you get 2y=1978 and y = 989 which makes z =414 and thus x is 180 (the speed of the cargo) and x+250 = 430mph (the speed of the jet)
T is 1st train ....
t (90) + t-1(100) =
90 t = -100 t + 100
-100 = -10t ......... t=10hrs
.................................................................................
r = rate
r(2.3) + (r+ 250)(2.3) = 1403
2.3r + 2.3r + 575 = 1403
4.6r = 828 ......................r =180
180(2.3) + 430(2.3) = 1403
414 + 989 = 1403 .........
100h=90h+90
10h=90
h=9
9 hours
not enough information