To attend a family reunion, Beth drives 100 mi from Fresno and Clara drives 220 mi from San Jose. Both women drive the same speed in miles per hour, but Clara's drive takes 2 hours longer than Beth's. Find the length of Beth's drive.
a. 1 hour. b. 2.2 hours
c. 1.66 hours d. 3.66 hours
distance = rate * time
100 = Beth rate * t
220 = Clara rate *(t+2)
BUT
we know that the two rates are the same, call it v
100 = v * t
so
v = 100/t
and
220 = v * (t+2)
or
220 = (100/t)(t+2)
220 t = 100 t + 200
2.2 t = t + 2
1.2 t = 2
t = 2/1.2 = 1 .67 hours which is 1 hour and 40 minutes
Thanks
To solve this problem, we need to set up an equation using the given information and variables.
Let's assume the speed of both Beth and Clara is x miles per hour.
Beth's drive takes t hours to complete, so her distance can be calculated as:
Distance = Speed * Time
Distance = x * t
Clara's drive takes 2 hours longer than Beth's, so her time can be represented as t + 2. Using the same formula as before, her distance is:
Distance = x * (t + 2)
Given that Beth drives 100 miles and Clara drives 220 miles, we can equate these distances to the respective expressions using the variables we defined earlier:
x * t = 100 (Equation 1)
x * (t + 2) = 220 (Equation 2)
Now we have a system of two equations that we can solve simultaneously to find the value of x and t.
First, let's solve Equation 1 for x:
x = 100 / t (Equation 3)
Now substitute Equation 3 into Equation 2 to eliminate the variable x:
(100 / t) * (t + 2) = 220
Next, simplify and solve for t:
100(t + 2) = 220t
100t + 200 = 220t
200 = 220t - 100t
200 = 120t
t = 200 / 120
t = 1.66 hours
Therefore, the length of Beth's drive is approximately 1.66 hours.
So, the answer is c. 1.66 hours.