Answer:
28r + 8r + r = 55
Step-by-step explanation:
Some values you know (given or calculated) and some things you do not know.
RATE TIME DISTANCE
BIKE 2*8r 1.75
RUN 8r
SWIM r 1
Total 55
Give a variable to unknown running speed and fill in everything.
RATE TIME DISTANCE
BIKE 16r 1.75 28r
RUN 8r t 8rt
SWIM r 1 r
Total 55
Notice some trouble? WHY? I missed seeing the "ran for one hour". the variable t is KNOWN! This will be corrected here:
RATE TIME DISTANCE
BIKE 16r 1.75 28r
RUN 8r 1 8r
SWIM r 1 r
Total 55
Calculations used to fill out the graph:
Then her running speed was 8r,
and her biking speed was 2*(8r) = 16r.
Swimming for 1 hour, Jenny covered the distance of 1*r = r kilometers.
Biking for 1.75 hour, Jenny covered the distance of 1.75*16r = 28r kilometers.
Running for 1 hour, Jenny covered the distance of 1*2r = 8r kilometers.
Everything is filled and looks good. There is a sum of distances in just the one single variable, r.
Solve for r, and this is the swimming speed.
28r + 8r + r = 55
The total distance is given by the sum of the product of the individual
average speed and time.
Correct response:
The given parameters are;
Time duration for each activity;
Swimming = 1 hour
Biking = 1.75 hours
To run = 2 hours
Speeds;
Average biking speed = 2 × Average running speed
Average running speed = 8 × Swimming speed
Total distance = 55.5 kilometers
Required:
To write and solve a linear equation to calculate Jenny's average swimming speed, x
Solution:
x represents Jenny's running speed, we have;
Running speed = 8·x
Biking speed = 2 × 8·x = 16·x
Distance = Speed × Time
Therefore;
1 × x + 1.75 × 16·x + 2 × 8·x = 55.5
Which gives;
x + 28·x + 16·x = 45·x = 55.5
[tex]x = \dfrac{55.5}{45} = \dfrac{37}{30} = 1.2 \overline 3 \approx \mathbf{ 1.2}[/tex]
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