At 9:00 on Saturday morning, two bicyclists heading in opposite directions pass each other on a bicycle path.The bicyclist heading north is riding 4 km/hour faster than the bicyclist heading south. At 10:15, they are 40 km apart. Find the two bicyclists’ rates.
northbound bicyclist = 19 km/h; southbound bicyclist = 15 km/h
northbound bicyclist = 18 km/h; southbound bicyclist = 13 km/h
northbound bicyclist = 18 km/h; southbound bicyclist = 14 km/h
northbound bicyclist = 16 km/h; southbound bicyclist = 10 km/h
northbound bicyclist = 18 km/h; southbound bicyclist = 13 km/h
Carlos and Maria drove a total of 233 miles in 4.4 hours. Carlos drove the first part of the trip and averaged 55 miles per hour. Maria drove the remainder of the trip and averaged 50 miles per hour. For approximately how many hours did Maria drive? Round your answer to the nearest tenth if necessary.
2.7 hours
3.1 hours
2.6 hours
1.8 hours
To solve this problem, we need to find the amount of time Carlos drove and subtract that from the total time to find the amount of time Maria drove.
Carlos drove the first part of the trip and averaged 55 miles per hour. Let's represent the amount of time Carlos drove as x.
Carlos's distance = Carlos's rate * Carlos's time
Carlos's distance = 55 * x
Maria drove the remainder of the trip and averaged 50 miles per hour. The total time for the trip is 4.4 hours, so the amount of time Maria drove can be represented as 4.4 - x.
Maria's distance = Maria's rate * Maria's time
Maria's distance = 50 * (4.4 - x)
The total distance of the trip is given as 233 miles, so we can set up the equation:
Carlos's distance + Maria's distance = Total distance
55x + 50(4.4 - x) = 233
Simplifying the equation:
55x + 220 - 50x = 233
5x = 13
x = 2.6
Therefore, Carlos drove for 2.6 hours. To find the amount of time Maria drove, we subtract that from the total time:
Maria's time = 4.4 - x
Maria's time = 4.4 - 2.6
Maria's time = 1.8 hours
So, Maria drove for approximately 1.8 hours. Therefore, the answer is 1.8 hours.
To solve this problem, we need to set up a system of equations based on the given information.
Let's assume that the speed of the southbound bicyclist is represented by x km/h. Since the northbound bicyclist is riding 4 km/h faster than the southbound bicyclist, their speed can be represented by (x + 4) km/h.
From the given information, we know that the bicyclists passed each other at 9:00 and at 10:15 they were 40 km apart. This means that they traveled for 1 hour and 15 minutes, or 1.25 hours.
To find the distance traveled by each bicyclist, we will use the formula: Distance = Speed × Time.
The distance traveled by the southbound bicyclist is (x km/h) × (1.25 hours) = 1.25x km.
The distance traveled by the northbound bicyclist is (x + 4 km/h) × (1.25 hours) = 1.25(x + 4) km.
Since they passed each other on the bicycle path, the sum of their distances traveled will equal the total distance between them, which is given as 40 km. So we have the equation: 1.25x + 1.25(x + 4) = 40.
Now we can solve this equation to find the value of x, which represents the speed of the southbound bicyclist.