sam and nikki lie 206 km apart. at 8:00 am. sam started driving to nikki's house at 60km/hr. at 10:00 am nikki started driving to sam's house at 82 km/hr. at what time will they be 15 km apart?
let the time driven by Sam be t hrs
let the time driven by Nikki be t-4 hrs
distance covered by Sam is 60t
distance covered by Nikki is 82(t-4)
60t + 15 +82(t-4) = 206
142t = 206 - 15 + 328
142t = 519
t = 3.655 hrs = 3 hrs and 39 minutes
so they will 15 km apart at 8:00 + 3:39
or at 11:39 am
thank you
To find out the time at which Sam and Nikki are 15 km apart, you can set up an equation based on their respective distances from their starting points. Let's breakdown the problem and find the solution step by step.
Step 1: Determine the distance covered by Sam and Nikki individually until they meet.
- Sam started driving at 8:00 am, so at that time, he had not covered any distance yet.
- Nikki started driving at 10:00 am. To find the distance she covered until they meet, you need to calculate the time difference between when Sam started and when Nikki started.
- The time difference between 8:00 am and 10:00 am is 2 hours.
Step 2: Calculate the distance covered by Nikki in the 2-hour time difference.
- Since Nikki's speed is given as 82 km/hr, you can use the formula: Distance = Speed × Time
- Distance covered by Nikki = 82 km/hr × 2 hr = 164 km
Step 3: Set up the equation to find the remaining distance.
- Since Sam and Nikki started at different times, the time it takes for them to meet will be the same for both.
- Let's assume they meet after time 't' hours. At that time, Sam has traveled for (t + 2) hours.
- Using the formula Distance = Speed × Time, the distance covered by Sam is 60 km/hr × (t + 2) hr = 60t + 120 km.
Step 4: Solve the equation.
- The total distance between Sam and Nikki initially is given as 206 km.
- Now, we need to solve the equation (60t + 120) + 164 = 206 - 15 (since we want them to be 15 km apart).
- Simplifying the equation: 60t + 284 = 191
- Moving the constant to the right side: 60t = 191 - 284 = -93
- Dividing both sides of the equation by 60: t = -93/60
- Note that time cannot be negative, so this implies they will never be 15 km apart. Please check if there's an error in the problem statement.
Based on the calculations, it seems that there might be an error or inconsistency in the given problem statement. Please verify the information provided to find a valid solution.