Sarah walked at a speed of 3 miles per hour. Beneta rode her bicycle at a speed of 9 miles per hour. They both traveled the same distance, but it took Sarah 4 more hours than it took Beneta.
How many hours did it take Beneta?
I am somewhat confused on where to start with this math problem.
Beneta's time ---- t hours
Sarah's time ---- t+4 hours
distance gone by Beneta = 9t , using distance = rate x time
distance gone by Sahra = 3(t+4)
but they went the same distance, thus ...
9t = 3(t+4)
solve for t and you got it.
I know that d=r x t
and there is a formula for Constant Speed d=vt
3 mi/h=3mi/1hr
9 mi/h=9mi/1hr
But I am confused on what steps I need to take to solve the problem.
Hello. So you are saying that I would have 3(t + 4)=9t
3t + 12=9t
12=6t
t=2
Would this be the correct answer?
Reiny how did you know just by looking at the word problem to do 3 (t + 4)=9t?
I just took the sentence "They both traveled the same distance" and translated it into math
Look at my steps,
one distance was 9t and the other was 3(t+4)
but they are EQUAL, so
9t equals 3(t+4)
9t = 3(t+4)
To solve this problem, you can set up separate equations for Sarah and Beneta, and then find the value of the unknown variable, which is the time it took Beneta.
Let's start by assigning variables to the unknowns:
Let's call the time it took Beneta "t" (in hours).
Since we know the speed of Sarah is 3 miles per hour, we can use this information to calculate the distance traveled by both Sarah and Beneta.
For Sarah, the distance is equal to her speed multiplied by the time it took her, which is (3 * (t + 4)).
For Beneta, the distance is equal to her speed multiplied by her time, which is (9 * t).
Since they both traveled the same distance, we can set up an equation:
3 * (t + 4) = 9 * t
Now, you can solve this equation to find the value of "t" which represents the time it took Beneta.
3t + 12 = 9t (by distributing 3 to t and 4)
12 = 9t - 3t (subtract 3t from both sides)
12 = 6t (combine like terms)
t = 12 / 6 (divide both sides by 6)
t = 2
Therefore, it took Beneta 2 hours to travel the same distance.