Math  /  Algebra

QuestionSee your tevels
Helen just started training for her first triathlon. She worked out twice a day for 10 days. For her morning workouts, she biked mm minutes and ran 20 minutes. For her afternoon workouts, she biked mm minutes and ran 30 minutes.
Pick all the expressions that represent how long Helen trained. 20m+50020 m+500 10(m+20)+10(m+30)10(m+20)+10(m+30) 10m+50m10 m+50 m 10m+200+10m+30010 m+200+10 m+300

Studdy Solution

STEP 1

1. Helen's training schedule includes both biking and running sessions, with specific durations for each.
2. The morning workout includes mm minutes of biking and 20 minutes of running.
3. The afternoon workout includes mm minutes of biking and 30 minutes of running.
4. The total time for training over 10 days needs to be calculated for both morning and afternoon workouts.
5. We are tasked with identifying the correct expressions that represent the total training time.

STEP 2

1. Calculate the total duration for morning workouts over 10 days.
2. Calculate the total duration for afternoon workouts over 10 days.
3. Sum the total durations from both morning and afternoon workouts.
4. Compare the resulting expression with the given options to identify the correct ones.

STEP 3

Calculate the total duration for morning workouts over 10 days. Morning workout duration per day: mm minutes biking + 20 minutes running.
Total duration for morning workouts=10×(m+20) \text{Total duration for morning workouts} = 10 \times (m + 20)

STEP 4

Calculate the total duration for afternoon workouts over 10 days. Afternoon workout duration per day: mm minutes biking + 30 minutes running.
Total duration for afternoon workouts=10×(m+30) \text{Total duration for afternoon workouts} = 10 \times (m + 30)

STEP 5

Sum the total durations from both morning and afternoon workouts.
Total duration=10×(m+20)+10×(m+30) \text{Total duration} = 10 \times (m + 20) + 10 \times (m + 30)

STEP 6

Simplify the expression to find the total training time.
Total duration=10(m+20)+10(m+30)=10m+200+10m+300=20m+500 \text{Total duration} = 10(m + 20) + 10(m + 30) = 10m + 200 + 10m + 300 = 20m + 500

STEP 7

Compare the resulting expression with the given options:
1. 20m+50020m + 500
2. 10(m+20)+10(m+30)10(m + 20) + 10(m + 30)
3. 10m+50m10m + 50m
4. 10m+200+10m+30010m + 200 + 10m + 300

The correct expressions are:
1. 20m+50020m + 500
2. 10(m+20)+10(m+30)10(m + 20) + 10(m + 30)
4. 10m+200+10m+30010m + 200 + 10m + 300

The expression 10m+50m10m + 50m is incorrect because it does not correctly represent the sum of the training durations.

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