Natasha drove from Bedingsfield to Portsmouth at an average speed of 100 km/h to attend a job interview. On the way back she decided to slow down to enjoy the scenery, so she drove at just 75 km.h, Her trip involved a total of 3.5 hours of driving time. What is the distance between Bedingsfield and Portsmouth?
Let D=distance (one-way)
then
D/100+D/75=3.5
Solve for D.
50 mi
To calculate the distance between Bedingsfield and Portsmouth, we can use the formula:
Distance = Speed × Time
Let's break down the problem:
1. Natasha drove from Bedingsfield to Portsmouth at an average speed of 100 km/h. Let's denote the distance between Bedingsfield and Portsmouth as "d1" and the time taken to cover this distance as "t1". Therefore, we have:
d1 = 100 km/h × t1
2. On the way back, Natasha decided to slow down to 75 km/h. Let's denote the distance between Portsmouth and Bedingsfield as "d2" and the time taken to cover this distance as "t2". Therefore, we have:
d2 = 75 km/h × t2
3. The total driving time for the trip is given as 3.5 hours. Therefore, the sum of the time taken to go one way and the time taken to return should equal 3.5 hours:
t1 + t2 = 3.5 hours
Now, we have a system of two equations:
d1 = 100 km/h × t1
d2 = 75 km/h × t2
t1 + t2 = 3.5 hours
To solve this system, we need to eliminate one of the variables. Let's solve for t1 in terms of t2 using the third equation:
t1 = 3.5 hours - t2
Substituting this into the first equation, we get:
d1 = 100 km/h × (3.5 hours - t2)
Now, we substitute the second equation into the third equation:
(100 km/h × 3.5 hours - 100 km/h × t2) + t2 = 3.5 hours
100 km/h × 3.5 hours - 100 km/h × t2 + t2 = 3.5 hours
350 km - 100 km/h × t2 + t2 = 3.5 hours
Simplifying, we get:
350 km - 75 km/h × t2 = 3.5 hours
Subtracting 350 km from both sides:
-75 km/h × t2 = 3.5 hours - 350 km
Dividing both sides by -75 km/h:
t2 = (3.5 hours - 350 km) / -75 km/h
Calculating this, we find:
t2 = -3 hours
This negative value indicates that the direction of travel is reversed. Therefore, we take the absolute value:
t2 = 3 hours
Now that we know the value of t2, we can substitute it into the third equation to find t1:
t1 = 3.5 hours - t2
t1 = 3.5 hours - 3 hours
t1 = 0.5 hours
Now, we can calculate the distances:
d1 = 100 km/h × t1
d1 = 100 km/h × 0.5 hours
d1 = 50 km
d2 = 75 km/h × t2
d2 = 75 km/h × 3 hours
d2 = 225 km
Finally, the total distance between Bedingsfield and Portsmouth is the sum of d1 and d2:
Total distance = d1 + d2
Total distance = 50 km + 225 km
Total distance = 275 km
Therefore, the distance between Bedingsfield and Portsmouth is 275 kilometers.