Can u help me solve these with solutions please?
1.) Terry, a marathon runner, ran from her house to the high school then back. The return trip took 5 minutes longer. If her speed was 10 mph to the high school and 9 mph to her house, how far is Terry's house from the high school?
2.) At 2:00 pm, a car leaves town A and another leaves town B. The distance between two towns is 60 km. One car travels 10 kph faster than the other. The car passes at each other at 2:30 pm. How far does each travel?
3.) An alloy which weighs 118 kilograms is 10% silver. How much silver must be added to produce a metal that is 25% silver?
4.) How much decaffeinated coffee (assume this means 0% caffeine) and 50% caffeine coffee should be mixed to produce 25 cups of 40% caffeine coffee?
Answers
Given : return trip took 5 minutes longer. If her speed was 10 mph to the high school and 9 mph to her house,
To find : how far is Terry's house from the high school?
Solution:
Let say Terry's house from the high school = D Miles
Time Taken in going School = D/10 hr = 60D/10 = 6D Min
Time Taken returning from School = D/6 hr = 60D/9 = 20D/3 Min
20D/3 - 6D = 5
=> 20D - 18D = 15
=> 2D = 15
=> D = 7.5
Terry's house from the high school was 7.5 miles away
Speed of cars = S km/hr & S + 10 km/hr
Distance covered in 30 mins = 1/2 hr = 60 km
=> S(1/2) + (S + 10))(1/2) = 60
=> S + S + 10 = 120
=> 2S = 110
=> S = 55 km/hr
S + 10 = 65 km/hr
Each Covered Distance = 55* 1/2 = 27.5 km & 65*1/2 = 32.5 km
Alloy = 118 kg
Silver = (10/100)118 = 11.8 kg
let say Silver added = S kg
then (25/100)(118 + S) = 11.8 + S
=> 118 + S = 47.2 + 4S
=> 3S = 70.8
=> S = 23.6
23.6 kg silver to be added
Decaffine Coffee = D
50% Caffine Coffee = C
Caffine = 0.5C
Total = D + C
(40/100)(D + C) = 0.5C
=> 4D + 4C = 5C
=> 4D = C
=> D/C = 1/4
1 : 4
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