You have two unknown rates, so we need to develop two equations to solve for these unknowns (based on the information given on the problem statement):
5x + 10y = 725
x + y = 100
By substitution, we get:
5x + 10(100 - x) = 725
5x + 1000 - 10x = 725
-5x = 725 - 1000
-5x = -275
x = -275/-5 = 55
100 - 55 = 45
Thus:
The mechanic who worked for 5 hours charged his time at $55/hr, and the mechanic who worked for 10 hours charged his time at $45/hr.
To verify, plug and chug the results back into the original equations:
5(55) + 10(45) = 725
275 + 450 = 725
725 = 725 [OK]
55 + 45 = 100 [OK]
422₅ - 143₅ = 224₅
We convert each number to base 10.
So 422₅ = 4 × 5² + 2 × 5¹ + 2 × 5⁰
= 4 × 25 + 2 × 5 + 2 × 1
= 100 + 10 + 2
= 112₁₀
143₅ = 1 × 5² + 4 × 5¹ + 3 × 5⁰
= 1 × 25 + 4 × 5 + 3 × 1
= 25 + 20 + 3
= 48₁₀
So 422₅ - 143₅ = 112₁₀ - 48₁₀ = 64₁₀
We now convert 64₁₀ to base 5
64 ÷ 5 = 12 r 4,
12 ÷ 5 = 2 r 2
2 ÷ 5 = 0 r 2
Counting upwards,
So, 65₁₀ = 224₅
So, 422₅ - 143₅ = 224₅
Learn more about number bases here:
brainly.com/question/18653770
About 39 I belive but if I’m wrong then that’s
The Required ratio between the speed of the boat and speed of the water current is 8:3.
<h3>What is ratio?</h3>
In mathematics, a ratio indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six.
Given:
Upstream time= 8 hr 48 = 8 4/5 hour
Downstream time= 4 hour
Let the man's rate upstream be x kmph and that downstream be y kmph.
Then,
distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs.
x* 8 hr 48 min = y* 4 hours
x* 8 4/5= 4y
y= 11/5 x
Now,
Required ratio
(y+x)/2:(y-x)/2
= (16x/5 * 1/2): ( 6x/5 *1/2)
=8/5:3/5
=8:3
Hence, the required ratio is 8:3.
Learn more about ratio here:
brainly.com/question/13419413
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