We have that El Paso is 320 miles from Tucson and 720 miles from San Diego.
You're travelling from Tucson to San Diego.
First we have to find the distance from Tucson to San Diego. We can do this by finding the difference between the distance of Tucson from San Diego and El Paso from San Diego.
That is:
720−320
400 miles
You leave by 6:00 am.
You drive for 75 miles per hour in 4 hours for the first part of the journey.
You then drive for 50 miles per hour for the rest of the journey.
The first step is to find the distance that the rest of the journey took. We can do that by first finding the distance covered in the first part of the journey and subtracting that from the total distance (400 miles).
To find the distance for the first part of the journey, we apply the formula for speed (rate of change of distance with time):
s = d/t
⇒d = s⋅t
where d= distance; t = time
Therefore:
d=75⋅4
d=300 miles
The first part of the journey covered 300 miles. This means that the rest of the journey covered:
400 - 300 = 100 miles
Now, to find the time the rest of the journey took, we have to apply the same formula for speed:
s=d/t
t=d/s
Therefore:
t=100/50
t=2 hrs
To find the total time it took to complete the journey, we have to add the times for the first part and the rest of the journey.
That is:
T=4+2
T=6 hours
Since you left home by 6:00 am, the time you will get to San Diego is 6 hours after that, i.e. 12 noon (Tucson time)
That is the answer.
