Please help me answer this!
At 1pm, two trains traveling towards each other leave from towns 312km apart. One train can travel at most 82 km/h, and the other train at most 74 km/h. What is the earliest possible time for the two trains to meet?
For this problem:
a. define variables
b. write an inequality that can be used to solve the problem
c. solve the inequality
just re-read your post and noticed you are dealing with inequalities.
Make the appropriate changes, the math doesn't change.
Reiny, do you know how unhelpful that is???????
To solve this problem, let's break it down step by step.
a. Define variables:
Let's define the following variables:
- d: the distance covered by the faster train (train 1)
- t: the time it takes for the faster train to cover the distance d
b. Write an inequality that can be used to solve the problem:
Since the two trains are traveling towards each other, the distances they cover will add up to the total distance between the towns, which is 312 km. We can write the following equation:
d + (312 - d) ≥ 312
(train 1's distance) + (train 2's distance) ≥ total distance
This inequality ensures that the total distance covered by the two trains is greater than or equal to the total distance between the towns.
c. Solve the inequality:
Let's solve the inequality step by step to find the earliest possible time for the two trains to meet.
d + (312 - d) ≥ 312
2d - d ≥ 312
d ≥ 312/2
d ≥ 156
Based on this inequality, the distance covered by the faster train (train 1) must be greater than or equal to 156 km.
Now let's find the time it takes for the faster train to cover a distance of at least 156 km, given that it can travel at most 82 km/h.
t = d / (train 1's speed)
t = 156 km / 82 km/h
t ≈ 1.9024 hours
Since time cannot be expressed in decimal parts, let's round up to the nearest whole number. Therefore, the earliest possible time for the two trains to meet is approximately 2 hours.
To summarize:
a. Variables: d (distance covered by train 1), t (time it takes for train 1 to cover distance d)
b. Inequality: d ≥ 156
c. Solution: The earliest possible time for the two trains to meet is approximately 2 hours.
let the distance travelled by the faster train be x km
let the distance traveled by the slower train be 312-x km
time for faster train = x/82 hours
time for slower train = (312-x)/74 hours
when they meet, wouldn't they have traveled for the time ??
so
x/82 = (312-x)/74
cross-multiply and solve for x
put that back into x/82