The distance between city a and b is 600 km. the first train left a and headed towards b at the speed of 60 km/hour. the second train left b heading towards a three hours after the first train left a, and it traveled with a speed of v km/hour. the trains met t hours after the time at which the first train left a. express v in terms of t. find the speed v if t=7; t=6.

Step-by-step explanation:

When the second train leaves, the remaining distance between the trains is ...

... 600 km - (3 h)×(60 km/h) = 420 km

That distance will be covered at the speed of (60 +v) so the time it takes for the second train to cover that distance is ...

... 420/(60 +v)

The variable t represents the time since the first train left, so is 3 hours more than this time value. Hence ...

... t = 3 +420/(60 +v)

Solving for v, we have ...

... t -3 = 420/(60 +v) . . . . subtract 3

... 60 +v = 420/(t -3) . . . . multiply by (60+v)/(t -3)

... v = 420/(t -3) -60 . . . . subtract 60

For t = 7 ...

... v = 420/(7 -3) -60 = 105 -60 = 45

For t = 6 ...

... v = 420/(6 -3) -60 = 140 -60 = 80

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)