The distance along a scenic route between cities is 344 miles. How long will it be before the two groups meet?

Question

The distance along a scenic route between 2 cities is 344 miles. 1 group of tourists left from the western end of the route at 40 mph. Another group left from the east at the same time, traveling in the opposite direction, at a speed of 46 mph. How long will it be before the 2 groups can expect to meet?

Answer 1

This is a systems of equations problem. 

The first driver is going at 40 mph so we sill say 40x

The second driver is going at 46 mph so we sill say 46y

We know that between the two of them they have to total 344 miles

so we will say 40x + 46y = 344 miles

We also know that the time that they travel must be equal since once they meet they will both stop so x = y

Now we can make this 40x + 46x = 344 miles since they are equal so that is 86x = 344

x = 4 hours

Answer 2

v = d/t ---> d = vt

 

The speeds are given. 

 

Their travelling time will be the same because they started and will stop at the same time.

 

t₁ = t₂; Let's just let the time as 't'.

 

The sum of the distances that they will travel should be equal to the distance between the cities which is 344 miles.

 

d₁ + d₂ = 344

 

v₁t₁ + v₂t₂ = 344

 

v₁ = 40, v₂ = 46

 

40t + 46t = 344

86t = 344

 

t = 4 hrs.