The average height of 3 plants is 105 cm. Plant A is twice as tall as Plant B. Plant C is 0.65 m shorter than Plant A. What is the height of Plant C?
Let's define the heights of the three plants:
Let Plant B's height be x cm.
Since Plant A is twice as tall as Plant B, its height is 2x cm.
Since Plant C is 0.65 m shorter than Plant A, its height is 2x−65 cm (since 0.65 m = 65 cm).
We are given that the average height of the three plants is 105 cm:
A baker had some tarts and cookies. He packed the tarts in boxes of 6 and the cookies in boxes of 10. He sold each box of tarts for $28.80 and each box of cookies for $22.20. Number of boxes of tarts sold is 4 times the number of boxes of cookies sold. He earned a total of $2198.40 from the sale of all the boxes of tarts and boxes of cookies. How many tarts did he sell?
Let's define some variables to represent the given information:
Let the number of boxes of cookies sold = x
Since the baker sold 4 times as many boxes of tarts as boxes of cookies, the number of boxes of tarts sold is 4x.
Step 1: Set Up the Total Revenue Equation
The revenue from selling the boxes is calculated as follows:
Each box of tarts sells for $28.80.
Each box of cookies sells for $22.20.
At 09 00 hour, Peter travelled from City A to City B at a constant speed of 80 km/h. Half an hour later, Timothy travelled from City A to City B at a constant speed along the same route. After Timothy travelled 240 km, he caught up with Peter. Timothy took 5 hours to travel from City A to City B. Find the distance between City A and City B.
Let's define the given information:
Peter starts traveling from City A to City B at 09:00 at a speed of 80 km/h.
Timothy starts traveling at 09:30, meaning Peter has a 30-minute (0.5-hour) head start.
Timothy catches up to Peter after traveling 240 km.
Timothy's speed is unknown.
Timothy takes 5 hours to travel from City A to City B.
Step 1: Determine Timothy's Speed
Timothy traveled 240 km while catching up with Peter. Let v be Timothy's speed in km/h.
Since he took 5 hours to travel the entire distance, the distance between City A and City B is:
Distance=Speed×Time=v×5
Now, let's analyze when Timothy caught up with Peter.
Step 2: Determine Peter's Head Start Distance
Since Peter traveled at 80 km/h and had a 0.5-hour head start, the distance he covered before Timothy started is:
Head start distance=80×0.5=40 km
Now, when Timothy traveled 240 km, let’s determine the time he took:
Time taken by Timothy=240÷v
During this same time, Peter also traveled further at 80 km/h, so his total distance traveled after Timothy started is:
Distance traveled by Peter=80×240÷v
Since Peter already had a 40 km head start, the total distance he traveled equals Timothy's 240 km: