Question

the distance between two stations is 340 km . two trains start simultaneously from these stations on parallel tracks to cross each other . the speed of one train is greater than 5km of other. if the distance between the two trains after 2 hours of their start is 30km find the speed of both the trains

Answer 1

distance(d)=rate(r) times time(t) or d=rt;t=d/r and r=d/t
Let r=rate (speed) of the first train
Then r+5=rate of the other
Distance first train travels in 2 hours =r*2 or 2r
Distance other train travels in 2 hours=(r+5)*2 or 2(r+5)
Now we know that the distance the first train travels (2r) plus the distance the other train travels (2(r+5)) equals 340-30 or 310 mi. So our equation to solve is:
2r+2(r+5)=310 mi get rid of parens
2r+2r+10=310 subtract 10 from both sides
2r+2r+10-10=310-10 collect like terms
4r=300 divide both sides by 4
r=75 mph---------------------------speed of first train
r+5=75+5= 80 mph---------------------speed of other train
CK
75*2+80*2=310
150+160=310
310=310

Answer 2

Answer:

Step-by-step explanation:

distance(d)=rate(r) times time(t) or d=rt;t=d/r and r=d/t

Let r=rate (speed) of the first train

Then r+5=rate of the other

Distance first train travels in 2 hours =r*2 or 2r

Distance other train travels in 2 hours=(r+5)*2 or 2(r+5)

Now we know that the distance the first train travels (2r) plus the distance the other train travels (2(r+5)) equals 340-30 or 310 mi. So our equation to solve is:

2r+2(r+5)=310 mi get rid of parens

2r+2r+10=310 subtract 10 from both sides

2r+2r+10-10=310-10 collect like terms

4r=300 divide both sides by 4

r=75 mph---------------------------speed of first train

r+5=75+5= 80 mph---------------------speed of other train

CK

75*2+80*2=310

150+160=310

310=310