A Study to Investigate How JNJ-39758979 May Affect the Plasma Levels of Methotrexate in Rheumatoid Arthritis Participants

Inclusion Criteria: * Diagnosis of Rheumatoid Arthritis Functional Class I-III according to the American College of Rheumatology criteria for at least 3 months prior to Screening * Have been treated with and tolerated oral methotrexate (taken by mouth) for a minimum of 3 months prior to screening, and must have been on a stable once-weekly methotrexate dose (taken as a single dose) between 7.5 and 25 mg/week for a minimum of 1 month prior to Day 1 * Participants may continue on stable nonsteroidal anti-inflammatory drug (NSAID) and/or corticosteroid background therapy for rheumatoid arthritis (RA) or stable therapies for other conditions as prescribed by physician, providing that the doses of such therapy are stable for at least 1 month prior to screening and will remain unchanged for the entire study duration * Medically stable on the basis of physical examination, medical history, vital signs, and electrocardiogram (ECG) performed at screening * Laboratory values within certain limits at screening and Day-1. Abnormalities consistent with those observed in patients with RA are permissible. Exclusion Criteria: * History of or current clinically significant medical illness as specified on the protocol, or any other illness that the investigator considers should exclude the participant or that could interfere with the interpretation of the study results * Have been treated with a monoclonal antibody for RA in the 3 months prior to enrollment or have had a serious infection within 2 weeks of the study treatment period * Except for methotrexate, treated with approved or investigational non-biologic disease-modifying antirheumatic drugs (DMARDs) during the 4 weeks or 5 half-lives prior to the first dose of JNJ-39758979, whichever is longer. These agents include, but are not limited to D-penicillamine, hydroxychloroquine, chloroquine, oral or parenteral gold salts, sulfasalazine, leflunomide, azathioprine, cyclosporine, tacrolimus and mycophenolate mofetil.