At 9: 00 on saturday morning, two bicyclist pass each other on a bicycle path. the bicyclist heading north is riding 5km/h faster then the bicyclist heading south. at 10: 30, (1.5 hours later) they are 49.5 km apart. find the two bicyclists’ rates.

Step-by-step explanation:

One rider's rate is xthe other is x+4

Once they pass each other, they travel for 1.5 hrs...and the combined distance they travel = 39 km

SoRate x Time = Distanceand we have

x(1.5) + (x+4)(1.5) = 39 simplify

1.5x + 1.5x + 6 = 39

3x + 6 = 39 subtract 6 from both sides

3x = 33 divide by 3 on both sides

x = 11 km/hr this si the slower rider's rate

x + 4 = 11 + 4 = 15 km/hr and this is the faster rider's rate

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.