Question

Real World Scenario:

Answer 1

The distance of a train from the city depends on the speed, the time of

travel, and direction of motion of the train.

Correct responses:

• Distance Train A is from the city: 750 - 75·t

• Distance Train B is from the city: 50·t

• After six hours, the two trains are the same distance from the city

• At that time both trains will be 300 miles away

1) From the time of departure of Train B to just before 6 hours after Train B's departure; 0 ≤ t < 6 hours

2) At time period, t > 6 hours

3) 250 miles

Method used to find the above response

Given:

The distance of train A from the city = 750 miles

Speed of train A = 75 mph

Time at which Train B leaves the city = When Train A is 750 miles from the city

Speed of Train B = 50 mph

Solution:

The equations are;

• Distance of Train A from the city is; x₁ = 750 - 75·t

• Distance of Train B from the city is x₂ = 50·t

When the train are the same distance from the city, we have;

750 - 75·t = 50·t

750 = 50·t + 75·t = 125·t

Therefore;

• $t = \mathbf{\dfrac{750}{125}} = 6$

The time it takes the two trains to be the same distance from the city is 6 hours.

Which gives;

• After 6 hours, the two trains are the same distance from the city.

The distance the trains will be after 6 hours is therefore;

750 - 75 × 6 = 300

The distance of the trains from the city after 6 hours = 300 miles

Therefore, we have;

• At that time both trains will be 300 miles away

1) The time period Train A is further from the city is before the first 6 hours elapse; 0 hours ≤ t < 6 hours

2) The Train B is further from the city after 6 hours of its departure from the city; t > 6 hours

3) The distance of Train A from the city after 4 hours is given as follows;

x₁ = 750 - 75 × 4 = 450

x₁ = 450 miles

The distance of Train B from the city after 4 hours is; x₂ = 50 × 4 = 200

x₂ = 200 miles

Therefore;

• The distance between the trains after 4 hours = 450 miles - 200 miles = 250 miles

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