Question

Josh and Mike live $13$ miles apart. Yesterday Josh started to ride his bicycle toward Mike's house. A little later Mike started to ride his bicycle toward Josh's house. When they met, Josh had ridden for twice the length of time as Mike and at four-fifths of Mike's rate. How many miles had Mike ridden when they met?

a) $4$
b) $5$
c) $6$
d) $7$
The sum of the digits of a two-digit number is subtracted from the number. The units digit of the result is $6$. How many two-digit numbers have this property?

a) $2$
b) $3$
c) $4$
d) $5$
Every day at school, Jo climbs a flight of $6$ stairs. Jo can take the stairs $1$, $2$, or $3$ at a time. In how many ways can Jo climb the stairs?

a) $8$
b) $13$
c) $21$
d) $34$

Answer 1

The distance Mike had ridden when they met cannot be determined based on the given information.

Step-by-step explanation:

In this problem, we need to determine how many miles Mike had ridden when he met Josh. We know that the distance between them is 13 miles. Let's represent the rate at which Mike rides as x miles per hour. Josh rides at four-fifths of Mike's rate, so his rate is (4/5)x miles per hour. We also know that Josh rode for twice the length of time as Mike, so if we represent the time Mike rode as t hours, then Josh rode for 2t hours.

The distance Mike rode can be calculated using the formula: distance = rate x time. Therefore, Mike's distance is xt miles. Since the total distance between them is 13 miles, we can set up the equation xt + (4/5)x(2t) = 13. Simplifying this equation, we get 5x + 16x = 65. Combining like terms, we have 21x = 65. Dividing both sides by 21, we find that x = 65/21.

To find the distance Mike had ridden when they met, we substitute the value of x into the equation xt. Substituting, we have (65/21)(t) = d. To solve for d, we need to know the value of t. Unfortunately, the given information does not provide the value of t, so we cannot determine the exact distance Mike had ridden when they met. Therefore, the answer is indeterminate.